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Nairaland Forum / Nairaland / General / Education / Why Is Any Number Multiplied By Zero Equals To Zero? (43227 Views)
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Re: Why Is Any Number Multiplied By Zero Equals To Zero? by TheGoodJoe(m): 3:07pm On Jan 14, 2021 |
Dtruthspeaker: Get the point. The question is about the result. 15 and 2 are not the result. They are the factors used for production. Not what is produced. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by TheGoodJoe(m): 3:08pm On Jan 14, 2021 |
nonut: Maybe it came out simple to you but not me. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by YakubuA: 3:09pm On Jan 14, 2021 |
uracefriend: zero is simply absence of anything 1 Like |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by mu2sa2: 3:14pm On Jan 14, 2021 |
Aucun:"Then you didn't multiply them naa". Yes, I agree I didn't and I keep my cars, but you're saying I now have zero cars because of a failed attempt at multiplying them. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by iWise(m): 3:16pm On Jan 14, 2021 |
It's a consequence of the fact that the set of all real numbers together with the binary operations "+" and "*" is a ring with unity - that is, a ring that has a multiplication identity (rings are some of the most basic algebraic structures). 0 is the additive identity in this ring and 1 is the multiplication identity,, and every element has an additive inverse - if a is an element in this ring, then -a is its addive inverse so a+(-a) = 0. For example -1 is the additive inverse of 1, so 1+(-1) = 0. Suppose b is an arbitrary real number, then by distributive property of a ring, b*0 = b*(1+(-1)) = b*1 + b*(-1) = b +(-b) = 0. 2 Likes |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Firstandonly(m): 3:17pm On Jan 14, 2021 |
STINOS:I go like sit close to person like u for exams |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by pquaver(m): 3:17pm On Jan 14, 2021 |
TheGoodJoe: Are you stupid or you did not go to school? All this ariaria boys who no finish primary school with China phone everywhere. So you don't know what a testimonial or recommendation is? So if I give you a recommendation it means I pushed you? As you are so you want to tell me nobody has recommended you for anything in your life? That is why you are a nobody and busy causing nuisance here on Nairaland? OK come for recommendations make we see if your life fit change. You can't give what you don't have. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by banio: 3:18pm On Jan 14, 2021 |
What does the word multiply mean. If You think a little, you would would know what the word "multiply" means. Multiply means in increasing a number in multiples. So if you want to increase a number by multiple of zero. Then the number will be zero. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Dtruthspeaker: 3:21pm On Jan 14, 2021 |
TheGoodJoe: Yes, But All Products come from the Fact of Production Exactly as your post here in Nairaland is a Product of the fact that you CERTAINLY used a phone/Computer, Internet Connectivity, Registration in Nairaland Membership, Login and Successful Submission of your comment by pressing "Submit". The Whole True View is that it is an Inseparable Process, your Post and comment did not just fall in here, you went through a process. I can safely say that in this world, all True Products, Come from Due Process and the Process and Products are an Inseperable Whole. For there is No Product without a Process in this world. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Aucun(m): 3:21pm On Jan 14, 2021 |
mu2sa2: I don't know what you're on about. But following your illustration, you didn't even attempt to multiply the cars, unless there was an insurance or warrantee on it/them. A clear case of you trying to multiply the car would be, investing it in MMM, MBA forex or 9jabet! Unless, there was a money back guarantee, you won't get the car(s) back the exact same way/numbers. PS. This is not about "you" oh! It could be me, anybody or just plain imaginary. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Xfuzzy(m): 3:23pm On Jan 14, 2021 |
Great question OP.. This is going to be a really long read, but it's worth it. This question is more of mathematics and thus requires sound understanding of the axioms of mathematics to make sense of what's going on. I don't want you to appeal to a physical interpretation by trying to relate this with something real, something you can touch or something you can relate with. Mathematics is beyond all of this. Alright, lemme introduce you to Abstract Algebra, or just Algebra. This is a field of study in mathematics that deals with algebraic structures (will explain what this means shortly) and the various operations that can be done in these algebraic structures. Basically, these structures are just abstract entities with well-defined axioms that describes them. Now for starters, you may be wondering what an axiom is. An axiom is a statement or proposition that is well accepted based on logical inference and is self-evidently true, but can not be proved. Now, something about axiom is that, it is the foundation of all of mathematics, infact all of mathematics is built on well-defined axioms, from these axioms, theorems and conjectures are built to produce everything we've ever known in mathematics. So without axioms, there is no mathematics. Second is, axioms can't be proved, so these axioms must be well thought out by mathematicians before they are established. So as a mathematician, you don't worry about whether or not an axiom is true cause all of that has been handled by mathematicians. You just agree that these axioms exists and are self-evidently true. So if you take this statement as an axiom "X is even" you don't worry yourself over whether X can be odd at times, you just go ahead and work with the assumption that "X is even" must be true. So with that out of the way, I think it's time to introduce some of the algebraic structures we have in abstract algebra. These are just 3 of them: Groups, Rings, Fields. I don't know if there are others cause I'm not a mathematics student. But the algebraic structure of concern for today is Groups. Now, what is a Group? A group, just like every other algebraic structure, is an algebraic structures with some well-defined axioms. Aha, now what makes a Group different from a Ring and a Field, it's the axioms that define these groups. These axioms are somewhat different for the different algebraic structures. That's exactly what makes them different. So a Group is essentially an algebraic structure that contains a set (just the usual notion of set you've learnt), say G, and an operation, let's call this operation *, with some specific axioms. Now what are those axioms. 1.) Closure 2.) Associativity 3.) Existence of identity element that's always unique. 4.) Existence of an inverse, that's also unique for each element in G. So a Group contains: a defined Set, say G, a single operation, say *, and some axioms that shows how these operations are carried out. Everything outside of these is meaningless to a group. It's from these concept that we'll build everything we know about a Group. First, what does a set have to do with this? and what is even an operation to begin with? A set is just a fancy name for a collection of stuffs, I'm sure you have an idea of what set is and have probably carried out some "operations on set". So we introduced a set to contain some stuffs, these are called elements of the set, and it's these elements that'll carry out these operations self, so it's really important. Now, what's an operation, an operation can be something like "addition", where you just add up two things together, "multiplication" where you're required to just multiply things, and so on. Now, the question is, what's the definition of addition and/or multiplication in the first place. Are there axioms for these two things, now that's exactly what this axioms will describe completely. So you see why it's important we do all these? Let's say our set G contains three elements, "a" and "b" and "c". To write this mathematically, we say: G = {a, b, c} and the operation on this group is called , *. Don't be bothered about what this operation is at all. Ohh, and mathematically, to write that a, b belongs in G, we say: a ∈ G and b ∈ G. Simple right? Now let's continue and explain what this axioms mean. The first Axiom is closure: Closure means that, when you take any two elements in the set G, an operation under those two elements will produce another element, and this new element belongs in this same group. Mathematically you write it this way: if a ∈ G and b ∈ G, then a * b is another element, that belongs in G, simple right? So that basically means "a" and "b" can't just be the only members in G, it keeps expanding as we take up more axioms. But this is basically what the axiom of closure is all about. Now moving to the second axiom, associativity. This particularly axiom involves three elements. Hence why I started out with three elements in G. So let's see what this axiom states. It goes like this. if a, b and c belongs in G, then: a * (b * c) = (a * b) * c. So what does this statement literary mean? It means that if I take two elements in a group for example, b and c, and I do an operation, *, under them, the closure axiom guarantees us that b * c, belongs in the group. Now, don't forget that b * c is just one single element in G, so if I do another operation with "a" under *, it'll give me another element in the group called a * (b * c) since we assumed that closure is true. Now, consider the other way, if I operate "a" and "b" first, then I combine this result with "c" it'll give me (a * b) * c, so the axiom is telling us that both these results are equal and the same. It's as simple as that, no more no less, trying to relate this with our five senses and physical reality just doesn't work. That's what the axiom says and that's what we must work with. Now for the third axiom, first in mathematics, when they say something is unique, it means there's one and only one of that thing. So identity element being unique means there can only be a single identity element in a group. Usually the identity element is symbolically written as "e". So we just agree with this convention and move on. Now what does being an "identity element" even mean. That's what the statement of this axiom is. We know that "a" belongs in G, also our new element, e, belongs in G, an identity element is something that goes this like this: a * e = e * a = a For all "a" that belongs in G What does this even mean, it simply states that when you operate any element in G, let's say element "a" for example, with the identity element "e" in whatever way, whether a * e or e * a, at the end of the day, it preserves "a", that is, "a" doesn't change at all. So if I operate element "b" with the identity element, the output is "b" if I operate "c" with the identity element, the output is still "c". You'll like to ask, have I seen something similar to this before, yes you have. Think of it, if the operation, *, is "addition", what's the identity element? It's 0 of course.. because when you add 0 to any number, it doesn't change that number. Lol, now the thing is, 0 was chosen to play this role in mathematics. It could've been given any other symbol but that symbol and name was just chosen. How about if that operation, *, is multiplication, what's the inverse of multiplication, it's 1 of course. Because when you multiply 1 by any number, the output is still that number. Aha, now let's not just stop here, there is one more axiom remaining. Now for the 4th axiom. This one is about another element again that's in G. Lets symbolise that inverse element with M. Now, here's what it means to be an inverse element under operation, *. a * M = M * a = e. Aha, what this means is that our set G contains an inverse element, M, which when operated with "a" gives the identity element. Now each element in its own inverse ohh, it's different from identity element where the whole set G share the same identity element. So "a" has its own inverse and is unique (which means "a" has a single inverse), "b" has its own unique inverse, "c" has its own too and so on. Now this may already look too abstract to you, is there something I can relate this with? Of course this is, now let's say the operation, *, we're talking about is addition operation. What's the inverse? That is? What's that element which when added to "a" will give the identity element for addition (which is zero) that element is simply (–a). And that's because we know that: a + (–a) = 0. So the inverse of 5 is –5, the inverse of 2 is –2. And so on. How about multiplication, does it have an inverse too? Yes it does, the inverse under the operation of multiplication is "1/a" for "a" and that's because when you multiply "a" and "1/a" it'll give you 1, which is the identity element under multiplication. Although if you assume that 0 belongs in this group G, under the operation of multiplication, it has no inverse. The reason is not farfetched. 1/0 is meaningless in mathematics and that's because division of any number by 0 is not allowed in mathematics. Now we are armed to the teeth and we can tackle your question more properly. Now that we know what a group is all about, to restate it so as to be sure, a group is a structure with a set G and a single operation, say *, that obeys all those axioms we stated. We can now ignore those flimsy pictures we were trying to paint with the "2 things in zero place OR zero in three places". Let's work with this algebraic structure at out disposal and figure it out once and for all. Let's say we have a group called (G, *), actually this is how groups are represented in mathematics. G is the set, and * is the operation under G. Now let's start with operation of addition, which is represented by +. So what is 1 + 0? Remember we said 0 is the identity element under +, and we said (identity element axiom) that: a * e = a, so 1 + 0 = 1. It's easy now to see that: 0 + 0 = 0. 1 Like |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by ThatFairGuy1: 3:24pm On Jan 14, 2021 |
proxitaly:Nigeria of your own you meant not ours. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Bolingua1: 3:25pm On Jan 14, 2021 |
koning: You are still thinking like the Op, there is a particular part of your brain you have not activated, and it is the reason why we can't achieve much here as far as productivity is concerned. You break even because you have added nothing to the existing, so you still have the existing. 1000 + 0 = 1000 While your productivity or negativity which is your profit or loss equal 0 1000 * 0 = 0. We need to think better than this, I see lots of Chinese and I don't know why they are doing better than us. It's annoying |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by francotunsco: 3:26pm On Jan 14, 2021 |
BobFischer:Hmnnn... Why isn't 3*0=3? When one potent person meets with an impotent, what will happen? The answer is zero! Even if the potency of the potent person is raise to power 10! |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by koning: 3:30pm On Jan 14, 2021 |
mu2sa2: Brilliant analysis. That is the crux of the matter. You multiplied it by nothing. And now they say " You lost everything" Galileo(not sure about the spelling) was beheaded because he said the Earth was round, NOT flat. Centuries later everybody agrees that the Earth is actually round. It takes one man. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Stubborn82: 3:30pm On Jan 14, 2021 |
Bolingua1: You see, genius are not normal people, the irony is that normal people can not tell if someone is genius, in fact normal people see genius as stupid people. The question of the op might sound stupid to ordinary mind, but it is a question that can spark unexpected idea. This is how Isaac Newton come up with the law of motion, haven't you read about the Newton law of motion? Newton was questioning the fall of an apple and felt why must the apple fall, why not stay or hung on the air, with this question in the mind of a man like newton, what happens next.......boom......aha! The law of motion was born, which has help to improve scientific research and technological development. 1 Like 1 Share |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by AiooAi: 3:33pm On Jan 14, 2021 |
If you multiply any number by BUhaRi= 0 E.g. 100,000 *BUhaRi = 0 |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Codes151(m): 3:34pm On Jan 14, 2021 |
How do you determine 0 in real life? |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by ericmor: 3:36pm On Jan 14, 2021 |
mu2sa2: Is the result it yielded not the numbers you have used to multiply. Ok, after which you multiply 7*0 wat those it give? Nothing result. But when you say 7*1 you still have the 7 result. U can't have 7naira and multiply it with 0 and get anything, is not possible. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by SweetDipBenny(m): 3:37pm On Jan 14, 2021 |
Mathematicians in houz i hail o |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Najdorf: 3:37pm On Jan 14, 2021 |
BobFischer:This is product of poor math teachers who just teach rules instead of showing the logic behind them Multiplication is just repeated addition. Think of it like this: 2x3=3+3 3x3=3+3+3 4x3=3+3+3+3 5x3=3+3+3+3+3 Now what is 4x0? From the examples 4x0=0+0+0+0=0 5x0=0+0+0+0+0=0 Simple. 1 Like |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Stubborn82: 3:38pm On Jan 14, 2021 |
Gabbriell: Am not talking about mathematics here, am concerned about what led to the question of op. Multiplication might be your interest, but for me, is the disruptive thinking. The disruptive thinking is what bring new idea, every modern business need a position of entrepreneurs just like the way we have the position for HR, GM, MD, CEO. That is the position that really matter to bring about improving productivity and gaining competitive advantage in the market place. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Najdorf: 3:38pm On Jan 14, 2021 |
BobFischer:Multiplication is commutative. a*b=b*a |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by studentofTruth: 3:38pm On Jan 14, 2021 |
BobFischer: It's a disruptive question like this that led Einstein to the Relativity Theory. While abstract thinking is a sign of intelligence, it is seen as a taboo in this part of the world (Africa and Nigieria in particular) — they will soon call you mad, crazy, etc. You may have to tone it down if you're living in this part of the world. "The only thing an African man thinks of is how to put money in his pocket and get a woman to produce children. Thoughts like creating solutions to problems in the world and how to build a better society is beyond his mental capacity." I have come accept this painful reality! Back to your question, I will attempt to explain it using Einstein's general relativity theory. "Everything is relative to something else." In the case of anything multiplied by zero giving a product of zero, that "zero" product is relative to the action and not the entities multiplied — the product being zero doesn't mean that the non-zero entity vanished. Let me explain with your oranges example: First scenario (10x0 = 0): You have 10 oranges to give out. The action here is "to give out 10 oranges." To complete this action, there must be 10 oranges to give out and someone or something to give them to. In this case, you have the 10 oranges, but there's nobody/nothing to give the oranges. Relative to the intended action — giving out 10 oranges — you have given out zero oranges. However, it does not mean that the entity (10 oranges) vanished. In other words, the fact that the second entity needed to complete the action is not there (value: 0) doesn't mean that the first entity (10 oranges) has vanished. It only means that the action cannot be carried out (value: 0). To put it as an equation: Entity1(Present) x Entity2(Absent) = Action(Absent) Second scenario (0x10 = 0): You want to give out oranges to 10 persons. The action is "to give out oranges to 10 persons." To complete the action, you must have both entities — the oranges to give out and the 10 persons you will give the oranges. But you have no (zero) oranges, so the action cannot be carried out. Relative to the action — giving out oranges — you have done nothing (zero oranges given out). However, this doesn't mean that the 10 persons vanished because there were no oranges. In other words, the fact that the other entity needed to complete the action is not there (value: 0) doesn't mean that the second entity (10 persons) has vanished. It only means that the action cannot be carried out (value: 0). To put it as an equation: Entity1(Absent) x Entity2(Present) = Action(Absent) The point I'm making is that, using general relativity theory, the product of any multiplication with zero relative to the action and not the entities in the multiplication. The absence of any of the entities means that the action cannot be carried out, but the other entities don't cease to exit. So, even in cases of 10x2x0 = 0, you can extend this logic to explain it. An example of everyday application of this can be seen in anything. If there's no patient to be operated, the surgeon carries out no surgery (zero action), but it doesn't mean that the doctor or his surgical skills have vanished. If a fund manager sees no good opportunity to invest in, no investment happens (zero action), but that doesn't mean that the fund manager or the cash has vanished. This is why cash is a component of any portfolio — it stays there waiting for the right opportunity to go make you more money. 2 Likes |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by koning: 3:40pm On Jan 14, 2021 |
[quote author=Codes151 post=98054700]How do you determine 0 in real life? [/quo In my opinion 0 is emptiness, vacuum, nothing, zilch. Does not exist. That's why that traditional way of multiplication is giving the Op and Me something to ponder about. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by studentofTruth: 3:41pm On Jan 14, 2021 |
Stubborn82: You are right, but in Africa, disruptive questions are tagged crazy! 1 Like |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by koning: 3:43pm On Jan 14, 2021 |
Codes151: In my opinion 0 is emptiness, vacuum, nothing, zilch. Does not exist. That's why that traditional way of multiplication is giving the Op and Me something to ponder about. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by TheGoodJoe(m): 3:57pm On Jan 14, 2021 |
pquaver:Abuses does not give you credence or rep. The fact is that Buhari was pushed a lot Even the military rule he made a mess of was handed to him on a platter. Other people carried out the coup. When it was over, he was luckily the one selected to rule. Not earned. You can abuse from today until tomorrow but the truth won't change. 1 Like |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Bolingua1: 3:58pm On Jan 14, 2021 |
Stubborn82: Well said. They made you want to think why things are the way there are. The ability to reason logically and come up with reasonable explanations, but the comments that to follow and the inability of some to not still get why, and couldn't understand why, is appalling. This is not what we should be discussing. So many inventions are still waiting for us, not just how to make money and feed family. |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Iconstar: 4:05pm On Jan 14, 2021 |
STINOS:You forgot to add "copied from quora" |
Re: Why Is Any Number Multiplied By Zero Equals To Zero? by Codes151(m): 4:09pm On Jan 14, 2021 |
koning: You(1) Pick up (3) onions: That is 3 x 1? You(1) Pick up (2) onions: That is 2 x 1? You(1) Pick up (1) onions: That is 3 x 1? You Pick up NOTHING: What is 1 x 0? If you have NOTHING, then NO onions is the same as ZERO Onions If you have nothing, 45 didn’t disappear, it just picked nothing Same thing applies in reverse! 1 bag to put 3 onions, 1 x 3 = 3 onions inside 1 bag to put 2 onions, 1 x 2 = 2 onions inside 1 bag to put 1 onions, 1 x 1 = 1 onions inside 1 bag to put 0 onions, 1 x 0 = 0 onions inside Nothing. QED |
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