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Episode 4 Today, in Episode 4, I concluded the topic of data structures by discussing lists, which are more complex data types compared to vectors (1-dimensional arrays), factors, matrices (2-dimensional arrays), and data frames. In the second part of the session, I covered conditional statements and logical operators, focusing on "if", "else", and "else if" statements. I wrapped up the session with an introduction to loops, specifically "while" and "for" loops, thus concluding the introductory part of the course. Starting next session, we will begin using packages, particularly the tidyverse. https://www.youtube.com/watch?v=-A4UqMEO4cw |
iamoyindamola:Naam thanks |
JazaakumuLlah khaera Amoto94: |
Muslims are encouraged to engage in social acts and acts of worship together: prayer in congregation is encouraged, going out on the day of “Eid” and giving salam to one’s fellow brothers and sisters is required, smiling at one’s brother or sister in Islam is a highly meritorious act, and even eating together brings blessings to Muslims. The concepts of unity and brotherhood are significant in Islam as anything that has the potential to bring together the hearts of Muslims and encourages them to be kind to one another is cherished as highly important. With regards to bringing together the hearts of people, there is something to be said about talking over food. The most scintillating conversations or heated debates can occur over spaghetti and meatballs or a cup of coffee with an interesting companion. Shared meals provide people with the opportunity to share what is on their minds, how their day has been going, or simply how they feel at the moment: a concept that is quite significant in this world of incessantly beeping phone notifications and daily schedules planned down to the minute. Life today can get pretty hectic when it comes to having free time, making it of the utmost importance that we human beings schedule time to sit and connect with our friends and families and regular conversation over meals seems to be quite the ideal way to accomplish that Eating together brings far more benefits than first perceived. Primarily, regularly scheduled family meals give families a specific time every day to share. This is important because hectic schedules of the twenty-first century have resulted in teenagers and children holing up in their rooms with their TV’s, laptops and iPods, while parents complain that their children never open up with them. Communication is the prime benefit in sitting down together as a family over dinner; through it parents gain the opportunity to know what is going on in the lives of their children and kids can feel that their parents are more than just two authoritative figures in their lives. Another benefit in eating together as a family is that it fosters positive feelings among people; anyone who has ever had a bad day and subsequently required some comfort food and the company of a close friend is a testament to that. Eating with loved ones creates a warm environment that makes it easier to open up, talk and be affectionate with one another. Many time all it takes is good food and good company to have a wonderful time and good food with loved ones can bring about an air of warmth, comfort and mutual love between members of a family and create more of a tight-knit relationship within a family. A benefit of eating together that is quite rewarding with regards to a person’s akhirah is the fact that eating together brings blessings in the food being eaten.Wahshi bin Harb (May Allah be pleased with Him) reported: Some of the companions of the Messenger of Allah said: “We eat but are not satisfied.” He said, “”Perhaps you eat separately.” The Companions replied in the affirmative. He then said: “Eat together and mention the Name of Allah over your food. It will be blessed for you.” [Abu Dawud]. In this hadith we are told of two things, if done together, result in Allah Almighty blessing our food and putting barakah in it: saying Bismillah, and eating with others. Family dinners have the potential to increase the barakah of our food, a great blessing only attained when eating together. This is also exhibited by the following hadith: Abu Hurairah reported that the Messenger of Allah said, “The food for two suffices for three; and the food for three suffices for four persons.” [Al-Bukhari and Muslim]. This hadith shows that if people share a small amount of food it will be sufficient for them because of the blessing Allah places in the food. In essence, the benefits derived from eating together are multi-fold and contribute to increased communication between members of a family, their good relations, as well as blessings and barakah being placed in their food. As Muslims, these benefits are added to the fact that a deed that brings a family closer to each other is one that is highly meritorious. Our beloved Prophet (upon Him peace and blessings) said, “He who desires ample provisions and his life be prolonged, should maintain good ties with his blood relations.” [Al-Bukhari and Muslim]. This hadith beautifully illustrates that when one is in the service of his/her family, one is doing an act worthy of reward from Allah, and aiming to strengthen the bonds of family is one of the best acts that can be done in order to receive blessings from Allah. Every deed in Islam is judged according to the intention behind it, and so it should not be so surprising that such an overlooked, commonplace and seemingly menial occurrence such as a daily family dinner has the potential to bring about so many benefits to one’s family life https://jamiat.org.za/revive-a-sunnah-eat-together/
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https://www.youtube.com/watch?v=ToFa5_sbjKg In Episode 3, I continued our discussion on data structures, focusing on additional structures such as factors, matrices, and data frames. While all of these, including the vectors we covered in the previous session, are homogeneous (as they can only contain one data type), data frames are heterogeneous, allowing for multiple data types. Before diving into the session, I demonstrated how to generate reports by knitting them into PDF/Word formats using R Markdown, which we have now adopted for our Lab submissions. |
📢 ANNOUNCEMENT Due to some technical issues, I'm afraid our weekly R101 - R Programming in Yorùbá may not hold tonight as scheduled unless I'm able to resolve the problem before class time. If not, I will make it up to you tomorrow by God's grace. I sincerely apologize for any inconvenience this may cause. Thanks for your understanding. ✍🏾 Lukgaf |
Today, let's review the second hadith in Umdatul Ahkam. For past reviews, see here Narrated Aboo Hurayrah: The Prophet () said, “Allaah does not accept prayer of anyone of you if he does Hadth (passes wind) till he performs the ablutionIt is very clear that Allaah does not accept the prayer offered without an ablution. Ablution is compulsory for the prayer. According to all the jurists and Imaams the prayer is invalid if it is offered without an ablution or offered without Tayammum in case if water is not available. It is same with all kind of prayers, whether it is obligatory prayer or supererogatory prayer. Is Ablution Necessary for Reciting the Qur'an? It is not obligatory to have ablution (wudu) to recite the Qur'an verbally. There is no authentic hadith stating that ablution is a must for the recitation of the Qur'an outside of prayer. Therefore, one can even perform prostration for a verse of recitation without ablution outside of formal prayers. The requirement for ablution applies only to prayer, and if one comes across a verse of prostration during prayer, the ablution made for the prayer suffices for the prostration as well. Similarly, a prostration made for thanksgiving does not require ablution. If anyone claims otherwise, they should provide authentic evidence from hadith. The Validity of Prayer if Ablution Breaks Before Completion Some people claim that if ablution breaks right before the salutation (tasleem) in the final sitting (tashahhud), the prayer is still valid. They cite the following hadith as evidence: Abdullah ibn 'Amr reported that the Messenger of Allah (peace and blessings be upon him) said: “When the imam completes the prayer and sits for reciting the tashahhud, and then his ablution becomes void before he speaks to anyone, his prayer becomes complete, and those who prayed behind him also complete their prayer.” What to Do if Ablution Breaks During Prayer If someone breaks their ablution during congregational prayer, they should discreetly leave the prayer by holding their nose and withdrawing to renew their ablution. Afterward, they must start the prayer again from the beginning. Holding the nose gives the impression that the person may be suffering from a nosebleed, so the congregation will allow the individual to leave without causing disturbance. This behavior reflects the Islamic teaching of hiding personal issues without broadcasting them to the public. This practice is not considered lying or showing off but is instead a display of good manners and a means of maintaining peace and order in the mosque. The Prophet (peace be upon him) taught this method, as narrated in the hadith by 'Aaishah: ‘Aaishah reported the Prophet (peace be upon him) as saying: "When any one of you becomes defiled during prayer, he should hold his nose and then turn away.” This illustrates a thoughtful approach to dealing with such situations in the most respectful and discreet way possible. |
Whoever memorises the Quran and acts upon it, Allah will reward him abundantly and honour him greatly. He will rise in status in Paradise to a level commensurate with what he memorised of the Quran. Praise be to Allah.Let's strive to memorize the Holy Quran. It is not too late! https://islamqa.info/en/answers/20803/reward-for-memorising-quran
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Episode 2 - data types and structures This week (Episode 2), I continued from where we left off in the previous session, where we explored how to use RStudio, the RStudio GUI and its functions, performed arithmetic operations in R, and introduced variables. In this session, I began explaining data types and structures, focusing on atomic or primitive data types—the simplest building blocks of the programming language, which include double, integer, character, and logical types. These were covered in the first part of the session. Since these building blocks can be combined within data structures to create objects containing data, I introduced the concept of vectors, which are one-dimensional, single-class data containers. https://www.youtube.com/watch?v=lvSfaVtHHQI |
We'll continue our weekly class, R 101 - Introduction to R programming in Yorùbá tonight at 9 PM Nigeria time. Please don't forget to join us. You can catch up on the last class below: https://www.youtube.com/watch?v=_LpwgrRd8O8 Thanks. |
Today, let's review the first hadith in Umdatul Ahkam. For past review, see here Narrated ‘Umar (bin Al-Khattaab): Allaah’s Messenger said, “The reward of deeds depends upon the intention and every person will get the reward according to what he has intended, So whoever emigrated for Allaah and His Messenger then his emigration was for Allaah and His Apostle. And whoever emigrated for worldly benefits or for a woman to marry, his emigration was what he emigrated for.”Fiqh of the Hadith The Prophet said this on the occasion of someone’s emigration from Makkah to Madeenah not for the sake of the Islamic Cause but to marry a woman who was called Ummul Qays, who had stipulated that he should emigrate if he wanted to marry her. Hence, he did migrate to Madeenah, and was titled emigrant of Ummul Qays because he married her. This hadeeth forms the sum and substance of the teaching of Islam. It is one of the fundamental principles of law in all ages. This hadeeth implies a general principle, i.e. one is rewarded for his deeds according to his real intentions not according to his actual deeds, which might be good in them but motivated, by an ill intention. The rewards for the Emigrants differ according to their intentions, i.e. whether they emigrated for worldly benefits or for the Pleasure of Allaah and His Messenger. The acceptance of an action for reward by Allaah depends on the nature of an intention for which an action is done. If the intention working behind and action is sincere and the action is done for seeking the countenance of Allaah, the action is accepted and rewarded by Allaah. Contrary to it, if the motive behind an action is to gain some worldly benefits or earn a good name in the world and there is no bit of sincerity in seeking the pleasures of Allaah, then the action will have no worth and weight in the Hereafter. Instead, the man will be punished for such action, as it is not based on good intention. In the Hereafter, everyone will be judged according to his intentions. Significance of sincere intention in the life The main object of the life of a Muslim, from the beginning to the end, is to achieve the pleasure of Allaah. All his energies should, therefore, be directed to the achievement of this single goal. The deed, however noble it may superficially appear, or task, however great and useful it may seem to the people, has no value in Islam if it is not done or undertaken purely for the love of Allaah. The work done for other means and ends, besides seeking the pleasure of Allaah, is valueless in Islam. Unfortunately, however, form has been more important nowadays than spirit, and religion has now become an unimportant thing in the life of human beings. This hadeeth is considered to be one of the great principles of the Divine Faith. It purifies the heart of a man from all kinds of impurities, e.g., mannerism, showing off, ignoble pursuits of life, love for wealth, power, pride, and vanity, and makes him a silent, honest, and untiring worker in the cause of Allaah, absolutely free from the love of low desires. This hadeeth also solves one of the problems of ethics pertaining to the relationship of ends and means.
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Can we insult, mock and lampoon people just for a joke? Praise be to Allah.https://islamqa.info/en/answers/472270/what-is-the-ruling-on-insulting-and-mocking-by-way-of-joking
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Episode 1 - Introduction | R studio This week, I began the weekly class with an introduction to the purpose of the session: why R programming? and why the course in our mother's tongue - Yoruba? The first part of the session focused on these topics. In the second part, I provided a preview of what to expect in the course and concluded the lesson by demonstrating how to use RStudio (an R IDE), explaining the R studio GUI & its functions, as well as performing arithmetic operations in R and introducing variables. https://www.youtube.com/watch?v=_LpwgrRd8O8 |
By God's grace, we're starting this course tonight. As earlier announced, the course is designed for beginners, covering the basics of R programming and data handling. As we are all aware, R is a powerful language for statistical analysis and data visualization. By the end of this course, you should be able to: - Program in R - Import and work with your own data files - Manipulate and summarize data entries with package such as dplyr - Create engaging visualizations with ggplot2 No prior programming experience is required. I'll provide example data files, and both R and RStudio software are free to download (I'll send instructions to download them soon). I hope we'll all enjoy the opportunity to learn R together in our mother's tongue - Yorùbá! |
🆕 ALẸ́ DÁTÀ: a week session on R Programming in Yorùbá! Exciting news! Our R programming class in Yorùbá is back, and this time, weekly (every Tuesday, 9pm Nigeria time)! Whether you're new to coding or looking to expand your skills, this weekly session is designed to empower you with the tools to excel in data science. In the pilot stage, I'll dive into: - Introduction to R Programming: Get started with the basics. - Data Manipulation & Visualization: Turn raw data into meaningful insights. - Statistics in R: Master the key concepts. And that's not all—future sessions will also introduce Python, making sure you have a comprehensive toolkit at your disposal. Get ready for engaging lab sessions where we'll practice hands-on coding and tackle challenging exercises together. Don't miss out on this unique opportunity to learn R programming in a way that resonates with you - in Yoruba. Let's embark on this data journey together
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As a Muslim, we should strive to better everyday. Below are ten things to do to become a Better Muslim. 1. Do Things/ Make Intention In The Name Of Allah.https://jamiat.org.za/ten-things-a-muslim-can-do-to-become-a-better-muslim/ Add yours
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This week (Episode 79), I began the next program—Program 12 (starting from frame 1, page 663)—which serves as an extension of the topic on series. I covered power series and explained the mechanics of expressing a function as a power series, specifically focusing on the Maclaurin series, where the terms are derived from the function's derivatives. https://www.youtube.com/watch?v=fYl_L26zv_8 |
Episode 24 - tangent as the ratio of sine and cosine functions https://www.youtube.com/watch?v=Wr__P60M7ag |
Seems Op used LLM 😂 "...highlighting the common fear of wrongful accusations and the harsh consequences that could have followed. ...This incident underscores the high-pressure environment healthcare workers often operate in" |
Let's start the first Chapter: BOOK OF PURIFICATION Significance of Purification in Islam: Islam laid a great emphasis on cleanliness of body along with cleanliness of mind because the former leads to the latter. The Glorious Qur’aan stressed a great emphasis on cleanliness and purification. Its significance is mentioned in the Glorious Quraan: “In it there are men who like to remain pure. Verily Allaah loves the pure ones”. At-Tuawbah: 9: 108. “O one clothed! Arise and warn, and Thy Lord do magnify, and cleanliness do shun”. Al-Muddathir: 74: 1-5. “O you who believe! When you rise up to prayer, wash your faces and your hands…” Al-Maidah: 5: 6. Purification leads one the Paradise The Prayer is compulsory upon every Muslim, man or a woman who reached the stage of puberty. The one, who does not offer five daily prayers after reaching the stage of puberty, is considered disbeliever according to the majority of the jurists and Imaams. Most naturally, the one who does not offer five daily prayers will never take of purity of his body, cloth, or place. Thus such person will be put to the Hell-Fire. Most naturally, the one who offers five daily prayers will be very careful about the purity of his body, cloth, and place. Thus, such person will most certainly go to the Paradise. The Prophet has also stressed great emphasis on purification and cleanliness of the body, clothes, and place. Purification of the body, cloth, and place is one the main conditions for validity of the Prayer. The Prayer in one of the five pillars of Islam, and it is compulsory to take bath before prayer in case of impurities, and wash of all exposed bodily limbs before each prayer. Islam emphasizes on cleanliness that the Prophet said that no prayer is accepted without purification of bodily impurities, and that cleanliness is half of faith and that it is the door to Paradise. The Prophet said: Cleanliness is half of faith…” The object is to keep oneself pure externally and internally. External purity leads to internal purity. One can only be healthy if he regularly keeps himself clean. Hence, to pray five times a day one has to perform ablution to offer the prayer. This is one of best way to keep oneself pure and clean. To be continued next week InshaAllah |
Assalam Alyakum, following the completion of our weekly review of " forty hadith of An-nawawih", let's start a new beneficial book "UMDATUL AHKAM MIN KALAAMI KHAYRIL ANAAM" by BY AL-IMAAM AL-HAAFIZ ‘ABDUL-GHANEE IBN ‘ABDUL WAAHID AL-MAQDASEE (541-600 HIJREE). I'll be following the exposition from the book by DR. ‘ABDUL MAJEED ‘ALEE HASAN. About the book 'Umdatul Ahkam is a famous text that contains hadith pertaining to juristic rulings (ahkaam) from Bukhari & Muslim written by Imam Abd Al-Ghani Al-Maqdisi.Source May Allah make it easy for us to complete this book and grant us its understanding. |
Praise be to Allah. Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) explained that showing off (riya') in worship can manifest in three different ways: 1. When the main motive for the act of worship is to be seen by others For example, someone prays or performs a good deed solely to gain praise from others. This invalidates the entire act of worship because it was not done sincerely for Allah. 2. When the idea of showing off develops during the act of worship Here, the person starts the act with sincere intentions but, during the act, the desire to show off emerges. This can happen in two ways: - No connection between the first and last part of the act: If the sincere part is separate from the part tainted by showing off, the first part remains valid, while the part influenced by showing off becomes invalid. *Example*: A man gives charity sincerely, but later feels the desire to show off. The initial charity is accepted, while the latter part is invalid. - The first and last part are connected: If the person starts sincerely but gives in to showing off before the act is completed, the entire act of worship becomes invalid. However, if they recognize the desire to show off and reject it, the act remains valid. Example: A person prays sincerely but starts showing off during the second rak'ah. If he gives in to this, the whole prayer is invalid. If he resists, it remains valid. 3. When showing off arises after completing the act of worship If the desire to show off arises after the act is completed, it does not affect the validity of the worship. Similarly, it is not considered showing off if a person feels happy that people have noticed their good deeds after the act is done. This natural joy is a sign of faith, as the Prophet (peace and blessings be upon him) said: "Whoever feels happy because of his good deeds and sad because of his bad deeds, that is the believer." Conclusion: Showing off in worship, whether before, during, or after, can affect the validity of the act depending on the timing and whether the person resists the urge. Sincerity is key in all acts of worship. May Allah grant us sincerity to do whatever we're doing for His favour alone (Aameen) Reference: Majmoo’ Fatawa al-Shaykh Ibn ‘Uthaymeen, 2/29, 30. Inspired from IslamQA
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This week (Episode 78), starting from page 652, Program 11, frame 33, I continued with other tests for convergence, including the comparison test, D'Alembert's ratio test, and absolute convergence. I demonstrated how to apply these tests to determine whether a series converges or diverges. This episode concludes Program 11. https://www.youtube.com/watch?v=MqIUnx5euok |
One thing that used to astonish me is the exorbitant amounts we budget for certain projects, which often reflect a lack of prudence or the misallocation of scarce resources to frivolities. Let me give you two examples. Earlier this year, I read a breakdown of the Senate's approved budget by BudgIT as published by IntelRegion. It allegedly showed that N82.5bn was allocated for the construction of 427 boreholes. This means that each borehole would cost N193m. If true, imagine the number of boreholes that could be constructed with that amount, especially since large-scale projects should be more cost-effective. The sad part is that many boreholes constructed under similar circumstances often stop functioning just a few months after being commissioned. Two weeks ago, I read that the Federal Government plans to spend N36bn to convert 30,000 petrol or diesel-powered vehicles to run on Compressed Natural Gas within 90 days. The conversion kits and associated costs were valued at N1.2m per vehicle, yet a screenshot of the kit's actual price (sent to a WhatsApp group I belong) showed it to be less than 500k. Had there been more prudence, we could have purchased more kits, benefiting a larger number of people. I also recall the outrageous amount said to be budgeted for feeding dogs, to mention just a few instances. What's worse is that people aren't even ashamed to present these inflated figures in public. How do we curb this corruption? I believe it starts with treating government money and properties as our own. We all negotiate and ensure we get quality at a lower price when buying things for ourselves, so why don't we apply the same principles to collective resources? Gafari Lukumon
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Praise be to Allah. Allah, may He be Exalted, has mentioned women who are forbidden in marriage because of kinship. Allah says (interpretation of the meaning): “Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters…” [An-Nisa’ 4:23] Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: These are seven who are forbidden in marriage, according to the text and scholarly consensus; none of the scholars differed concerning this." (Al-Sharh Al-Mumti`, 12/53) They are: The mother, which includes grandmothers on both the father’s and mother’s side The daughter, which includes granddaughters Sisters , whether full sisters or half-sisters through the father or mother The paternal aunt, which also includes the paternal aunt of the father or mother The maternal aunt , which also includes the maternal aunt of the father or mother The brother’s daughter, which includes his granddaughters The sister’s daughter, which includes her granddaughters Any other women who are relatives, apart from these, are permissible for marriage. Hence Allah, may He be Exalted, says in the following verse (interpretation of the meaning): “All others are lawful…” [An-Nisa’ 4:24] Based on that, the daughter of one’s paternal uncle or aunt, or of one’s maternal uncle or aunt, are permissible in marriage. The Quran states that in the verse (interpretation of the meaning): “O Prophet (Muhammad )! Verily, We have made lawful to you your wives, to whom you have paid their Mahr (bridal money given by the husband to his wife at the time of marriage), and those (slaves) whom your right hand possesses - whom Allah has given to you, and the daughters of your paternal uncles and the daughters of your paternal aunts and the daughters of your maternal uncles and the daughters of your maternal aunts…” [Al-Ahzab 33:50] Based on this, it is permissible for a girl to marry her father’s paternal cousin , because a person’s paternal uncle is an uncle to him and to all his offspring. So her father’s paternal uncle is also an uncle to her, and his son is her cousin, and it is permissible for a girl to marry her paternal cousin. it is also permissible for your daughter to marry the son of your mother-in-law’s brother, because the brother of your mother-in-law is her maternal uncle, because he is the maternal uncle of her father, and the maternal uncle of one’s father is also an uncle to his children. And it is permissible for a girl to marry her maternal cousin. And Allah knows best. https://islamqa.info/en/answers/161629/women-forbidden-for-marriage-in-islam-due-to-kinship
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Episode 77 - Series of powers of the natural numbers In this episode, starting from page 645 (Program 11, frame 15), I continued with the derivation of formulas for the series of powers of natural numbers and demonstrated how to manipulate them to evaluate various series. I concluded the video by discussing convergence and divergence, along with the tests used to assess them. https://www.youtube.com/watch?v=nZ-HhdZnWFw |
Forgiveness?https://jamiat.org.za/forgiveness/ |
Nobody likes bad leaders, poor governance, or insecurity. We all desire to live safely in our country, find employment, conduct our businesses with ease, and enjoy the resources that Allah has blessed us with, just like people in other countries. However, when we have leaders or live in a country where we don't enjoy these benefits, protesting or rebelling against the ruler is not always the solution. Many real-life incidents confirm that such actions often worsen the situation rather than improve our well-being and governance. A typical example is what happened during the 2020 EndSARS protest in Nigeria, as well as in Sudan, Kenya, and other places where protests led to more chaos. Why people should refrain from protesting? The basic principle of Shariah is that it is not permitted to remove an evil by means of a greater evil; evil must be warded off by that which will remove or reduce it. Warding off evil by means of a greater evil is not permitted according to the scholarly consensus (ijmaa’) of the Muslims.IslamQA Strikes and protests can result in greater trouble, leading to chaos, oppression, and the assassination of innocent people. This has been observed in states like Kano, Borno, Kaduna, and Yobe yesterday. What is the solution? We should all fear Allah – both leaders and followers. Often, we deserve the kind of leaders we have because we, the followers, are even worse. I watched a video of some guys destroying a traffic light. How does protesting justify destroying properties? You complain of bad governance, yet you destroy the little you enjoy? أفلا تعقلون؟ (Will you not reason?) Our leaders should remember that they will stand before the Lord of the worlds and account for whatever they have done, including how many lives were lost or people suffered as a result of their bad policies. Where are the past bad leaders? They are no more, and you too will be no more one day. So, a good leader should reflect on this. Umar (رضي الله عنه) said during his regime that if a horse stumbled due to bad roads, he would be held accountable for it. That's why records show that he and other past leaders would sneak into people's houses at night to check on their affairs. Our leaders should emulate this. Advice to Those Close to Leaders Those who are close to the leaders – their advisers and assistants – should fear Allah and tell them the truth. Many are sycophants who tell the leaders what they want to hear, lying that everything is good for their own benefit. They should remember the day they will stand before Allah and that whatever prestige or wealth they accumulate will end in this world. Leaders should be ready to listen to the truth. Role of the Elites and Religion leaders Our elites and those close to our leaders should explain the situation and advise on how it can be resolved. They should not leave them! May Allah bless our country. Abu Afs Lukgaf |
Episode 76 - Series 1 https://www.youtube.com/watch?v=LV3XT3fvuj8 Tonight (episode 76), I commenced Program 11 (page 640) of the book with the topic of series. In this session, I explained how to manipulate arithmetic series, geometric series, and series of natural numbers. These concepts will help us understand how to determine the limiting values of arithmetic and geometric series and apply various convergent tests to infinite series, which we will cover in the upcoming session. |