Why is any number multiplied by zero 0 ❓ A mathematical proof using the properties of real numbers.

[@puzzled8820]

This is what boredom has brought me too.

[@alexober9684]

What a nice and rigurous explanation!! We sometimes may assume the basic properties of multiplications we have been taught at school but even the most basic facts must be demonstrated in maths!!

[@discovermaths]

Many thanks. Yes, it's good to explore the foundations of what we sometimes take for granted.

[@yashaswikulshreshtha1588]

@@discovermaths I dont consider the method a reason for why, well its a same thing in maths if u expand a term with some properties and then derive it back then obvious ur gonna get same result just like adding a certain number to both sides on lhs and rhs and then substracting them both again to get answer...

[@giulialosi4805]

I am about to turn 48 this year and today on the subway I heard a 4yo ask his mother Explain me, why 5×0=0, and I realise I have no clue whatsoever about it. I stare at him appreciatively, he was even an immigrants' son and he was speaking our language, not his mother language. Excellent video, plain, simple, without paraphernalia of any sort, just the answer I need, thank you.

[@itsiwhatitsi]

I love this kind of explanations: a rigorous use of math properties to demonstrate something that we just take for granted: “a number multiplied by zero is zero” if the properties are true than we can logically derive these passages without doubts and make a real demonstration. Demonstrations are truly a next level of knowledge for humans, like a use of the logic in its purest form.

[@juancruzarruabarrena7567]

A very clear explanation. Thank you very much!

[@discovermaths]

Many thanks, Juan!

[@TerrorTarun]

Try 70-70*70*2*0

[@paulneamtu1373]

You could say easier that a * 0 is 0 because a * 0 means 0 + itself a times, and 0 plus itself how many times is 0, so any number * 0 is 0

[@EliasRiveraReal]

Multiplication is best tied to addition not as its repeated application, but through the distributive property. That way it's defined across all real numbers

[@Birdieeeeee]

So, When nothing is multiplied by something it gives nothing?? We can convert something into nothing?

[@totvabe1]

Clearly explained! Looking forward for the next video.

[@discovermaths]

Thank you. We'll be adding videos on a regular basis.

[@Gabriel-jp5dl]

Concise and superb explanation without going on tangents. I love this proof.

[@jcrakpilot]

A nice, clear and rigorous explanation !!

[@discovermaths]

Thank you very much!

[@ferus5583]

Thanks sir, but is there a practical example that gives me intuition to it?

[@ToxicAvengerCleanYourMind]

What happens when you apply it to real properties though? If I'm going 10 mph and I multiply it by 0, could not I still be traveling at 10 mph? Why does zero supercede the whole number absolutely?

[@discovermaths]

Because if whatever speed you're travelling at, if you travel at it for 0 seconds (say) you'll have covered zero distance. The principle works just as well with real quantities as it does with purely mathematical ones.

[@self-proclaimedanimator]

@@discovermaths Wow sir thnx for this example it helped me understand the video better

[@angelmendez-rivera351]

@@shamgarcahn9980 No. As the video demonstrates, why 1·0 = 0 as opposed to 1·0 = 1 has nothing to do with language. Human languages are not rigorous, and not even logically consistent. As for the topic of increase, an increase is an addition, not a multiplication, generally speaking. You increase the number of rabbits by adding rabbits. Adding a certain amount of rabbits per generation is equivalent to a scalar multiplication in certain contexts, but only because multiplication is reducible to addition in those contexts.

[@jonsupp1744]

Real things , i havent yet met anything that can prove me wrong. ex " I GOT 1 BEER IN MY HAND FACT. TIMES MY 1 BEER BY ZERO WAITIN."

[@ashleybyrd2015]

​@@jonsupp1744I can easily multiply the amount of beer in your hand by 0, all I need to do is steal it from you :)

[@ManishKumar-mv1zh]

It would be very helpful if you could please advise the important things one should keep in mind while writing proof in real analysis and algebra ?

[@discovermaths]

That's an extremely broad question. You need to study lots of other proofs to see how they're constructed. Determine what principles and hypotheses you're starting from, and make sure you understand every lemma and theorem that might be relevant to the proof. Know precisely your goal and try to identify any results that will help you get to your objective.

[@ManishKumar-mv1zh]

@@discovermaths Thanks 👍

[@vijay_r_g]

You know , actually I proved it using proof by contradiction,but this is more beutiful

[@Glicksman1]

A number multiplied by zero is zero because zero has no value and literally means "nothing", signifying "there is no thing." Accordingly, when we write, "A x 0" , we are really writing, "A, zero times". A, zero times is, of course the same as "no As," or "zero As". Since A has a value (unless A = 0), "no As" signifies no value, or zero. Thus, A x 0 = 0 QED.

[@EliasRiveraReal]

0 is defined as the additive identity. That is, by the property that for all numbers x, x+0=x

[@AitorGude]

Great video, thanks!!

[@discovermaths]

Thank you - that's very encouraging!

[@charlesbouvette2055]

I am slightly confused. I thought for a mathematical equation to be true , it must be workable in reverse. Therefore 10X0=0 couldn't be true because 0/0 can't equal 10

[@draconic7087]

of the the factors just tells us the number of times the other should be added. 10 repeated ZERO times is still zero. 10 repeated one time is JUST THAT NUMBER -i.e. 10*1=10=10 or 1*10=10=10. multiplication is shorthand for repeated addition, at least in elementary math.

[@Unknown__-]

Please excuse my ignorance if you have 12 pencils and you multiply them 0 times don't you still have 12 pencils on the other hand if you have 0 pencils and you multiply them 12 times you have 0 pencils please explain

[@discovermaths]

Think of 0 times 12 pencils as being the answer to the question: How many is 0 lots of 12 pencils?

[@jasber2916]

Shouldn’t 12 pencils times zero times be 12? This is why I probably struggle at math. Nice thing about math, it has to be proven. That’s something I can believe in.

[@vkrgfan]

@@Galax1ezX however 12 + 0 = 12 why addition makes 0 a valid value?

[@lucasignorelli5302]

@@jasber2916 As the author of this video said above, "12" would be the result of the question "How many pencils there are in 1 group of 12 pencils?" (12 x 1). "12 x 0" can be translated in "How many pencils there are in 0 (or "no") group of 12 pencils?". The answer is of course 0

[@lucasignorelli5302]

@@vkrgfan Because addition and multiplication are two different operation. Intuitively you can say that addition is "if I add 0 pencils (so, no pencil!) to 12 pencils, how many pencils do I get?. The answer course is 12. At the same time you can say that multiplication is "If I take 0 group of 12 pencils (so I don't take any group!) how many pencils do I get?". The answer is of course is no pencil at all.

[@abhinavshresth1798]

Superb Simple Smooth explantion

[@viswachaitanyasai4557]

Ur a genius

[@cagancao]

By simplifying, you actually divide 0 by 0, which you can't do.

[@EliasRiveraReal]

Are you talking about 1:50 ? Notice he used not division, but subtraction. a • 0 having been subtracted from both sides. Every number has an additive inverse, so any number may be used to subtract

[@surajkr.sharma448]

Sir please explain it. By ring theory 🙏

[@Claystation-ul7db]

If I have 1 apple in my hand and I multiply it by 0 then how many apples are in my hand??

[@angelmendez-rivera351]

0 apples.

[@YesYesYes1342]

@@angelmendez-rivera351 silly Babylonian

[@angelmendez-rivera351]

@@YesYesYes1342 I fail to understand how my answer makes me a silly Babylonian.

[@matijas7994]

wait,i need to ask something. As we know,multiplication and division are connected so for example 2×4=8 and 8÷4=2 so, 2×0=0 and 0:0=2?

[@discovermaths]

Division by 0 is undefined.

[@angelmendez-rivera351]

Multiplication and division are not connected in the way you say they are. Not all algebraic structures that have well-defined multiplication have division.

[@jasber2916]

I think that’s what our problem in society and numbers. There is never nothing (zero) , there’s always something. I hate the fact that we have a base for nothingness. There always is something.

[@intrepidelica7059]

Wrote 5 zero times and add it up... write 5 zero times and you get nothing.

[@angelmendez-rivera351]

I have 0 chickens. Therefore, your statement is completely wrong.

[@anukritijariwala4342]

Nice

[@discovermaths]

Thank you!

[@aljosia6525]

That's ridiculous. A x 0 should still leave you with A. Where in the real world can you multiply anything by 0 and get 0?!???

[@EliasRiveraReal]

Everywhere these axioms apply

[@ChickenPermissionOG]

isn't a*0=a+0?

[@hasnakhalifi9855]

I love this man

[@chessify518]

How to explain this to 2nd standard student

[@jacintanancy2659]

How

[@jorgeapg]

Gracias! :)

[@alfonsasspalviskis2651]

This video proofs that i cant understand math.

[@456death654]

And english

[@cyberspacer123]

In the real world though it does not make logical sense, If i have 5 dollars and multiply my 5 dollars zero times, I still have my 5 dollars.... not zero dollars, i simply have not increased it's value. Multiplication always increases value, why shou8ld zero break the rule and decrease the value? Should zero not behave more like 1 in this situation? (If you multiply any number of real objects in the real world by 0, they do not disappear, they simply do not increase).

[@456death654]

In the real world what you are saying is Multiplying $5 by 1. Because 1 is the amount of $5 in your hand hence why you still have $5. Multiplying implies you have zero of that item to begin with. Really easy

[@aceboogieceoboy8028]

so where do the A go? how do i have 100 dollars and multiply by 0 and end up with 0....where did my 100 dollars go?

[@EliasRiveraReal]

If your money were multiplied by 2, would you question where it came from? Or if you lost 5 dollars, where they went? It ultimately depends on context, but since multiplication by 0 is a bit more abstract it's best thought through using mathematical logic and axioms as demonstrated in the video

[@lbits]

😢I still don’t get it! Help!

[@thewayitis2012]

But if I have $100 and times it by nothing (0) it’s still $100 so makes no sense lol 😂

[@angelmendez-rivera351]

No. If you have $100 and you multiply that by 0, you obtain $0. Your calculations need improvement. I will give you 0 stacks of $100, and if you can still prove that this transaction somehow created $100 new in your bank account, then I shall eat a potato through my nose.

[@shamgarcahn9980]

@@angelmendez-rivera351 I think it's the lack of context that confuses people. He's saying if he multiplies his actual, physical $100 by 0, that $100 won't disappear out of his hand, he still has the $100. It's just what you said, he will obtain nothing more if it is only multiplied by 0. So the context of his equation is the increase of what was obtained, not what is left overall. That's what I was trying to convey in the comment that you responded to.

[@angelmendez-rivera351]

@@shamgarcahn9980 *He's saying if he multiplies his actual, physical $100 by 0, that $100 won't disappear out of his hand, he still has the $100.* I have to imagine that he does not really understand what it would mean to physically multiply something by 0. To be clear, taking your stack of $100, saying out loud "I multiply you by 0!" and waiting to see what happens does not amount to any actual type of multiplication at all. One of the best ways to visualize multiplication is with some hypothetical printing machine capable of cloning objects. If I put $100 on a printing machine and I click the "multiply by 5" button, the machine will take the $100, and transform them (somehow, let us forget about the laws of physics here for a second) into $500, or 5 stacks of $100. That is what multiplication looks like. If I click the "multiply by 0" button instead, the machine will simply evaporate the $100 into thin air, reproducing a grand total of $0 at the end. So, I have no idea how you would arrive at the conclusion that you still have $100. My hypothesis is that people do not actually understand how to physically visualize multiplication to begin with.

[@aceboogieceoboy8028]

real rap

[@BallisticallyJeff]

no this principle is not correct. If I have 0 and multiply it by 5 then I have 0. However if I have 5 and multiply it by 0, I still have 5. For example I have 5 slices of cake, and divide the pieces buy 5 people, Each person get 1 slice. If I have 5 pieces of cake, and divide it by 0 people, I still have 5 pieces of cake. It doesn't disappear. In the same respect if I have 5 dollars, and multiply it by 0, I still have 5 dollars. It did not multiply or disappear, it remained the same. If I had no dollars or 0 to start with I have nothing to multiply or divide so it remains zero. However in the instance of 5 x 0 the correct answer is 5. we have been thought wrong.

[@podometic]

Again, please start with a formal axiomatic definition of multiplication. As per Aristotle, you can't introduce undefined terms in a proof. Thank you.

[@angelmendez-rivera351]

He did start with a formal axiomatic definition of multiplication. He introduced multiplication as being defined by the axiom of distributivity. This was explained in the second half of the video.

[@chessify518]

How to explain this to 6 years old

[@alexbusoni]

I understand the conventions in mathematics with its not logical and very virtual property. The very essence of multiplication involves the synthesis of a new number from the sum of the enumerations of a digital value. That is, we have 5 planes multiplying them by 0, that is, by the number of planes of which we produced 0 at the factory, to those five planes and produced 0 planes. Of course, everyone will say that you need to put those five planes after, but as if these planes just stood next to the non-produced ones))) мне понятна условность в математике с её не логичным и очень виртуальным свойством. сама суть умножения подразумевает Синтез нового числа из суммы перечислений циферного значения. то есть у нас есть 5 самолётов умножая их на 0 то есть на кол-во самолётов которых на заводе произвели 0 мы к тем пяти самолёта и произвели 0 самолётов. конечно все скажут что те пять самолётов нужно после равно поставить но как если эти самолёты просто рядом с не произведёнными постояли)))

[@angelmendez-rivera351]

*I understand the conventions in mathematics with its not logical and very virtual property.* Mathematics are logical, because they are based in formal logic. *The very essence of multiplication involves the synthesis of a new number from the sum of the enumerations of a digital value.* False. Multiplication is not exclusive to numbers. Also, the essence of multiplication is the axioms of distributivity.

[@lisomdleleni5521]

You couldn't divide by ax0 because it is 0 and you can not divide by 0

[@angelmendez-rivera351]

He never divided by a·0.

[@joanfordham1305]

Well it doesn’t matter how many times you are given nothing. you still have nothing right ? Ask any politician

[@yedidyadoron4227]

You can't apply this to reality.

[@bigwill-ux3pz]

You proved 0x0 isa lie thanks 👍🏼 a x o bullshit 😂😂 u smoking some good weed professor youtube