Why is 0 times any number=0?

0 times, beginning at zero of course. you have to back into peanos axioms and increment from 0 as the basis of addition (iterative incrementation) and multiplication builds on that, as iterative addition.

ab is the volume of the rectangle with sides a and b.
a0 is the volume of the line segment of length a.

area*

F is a field.
0 ∈ F.
Let a ∈ F.
a*0 = a*(0 + 0) = a*0 + a*0.
(-a*0) + a*0 = (-a*0) + ((a*0) + (a*0))
0 = a*0.

Think of multiplication as "groups of"

2 groups of 3 is 6.

4 groups of 2 is 8.

0 groups of anything is obviously going to be 0.

Why does a + 0 = a
Why does a + (-a) = 0
Why does a + b = b + a
Why does (a+b)+c =a+(b+c)
Why does a(b+c)=ab+ac

Nobody knows it seems. We just accept these a logical facts of numbers. Isnt this insane? What is addition and multiplication?

They are games that someone made up one day with it's own set of specific rules/

Look, a common-sense answer that is more logical than all the maths shit itt

But then why do so many things adhere to these rules?

Except 0 groups doesnt exist. Whats a 0 group?

There is no group.

2 lots of 4 bananas is 8 bananas
1 lot of 4 bananas is 4 bananas
0 lots of 4 bananas is 0 bananas

>0 lots
this causes the mathfag to panic

because 0^0=1

That depends on accepting 0*0=0

So is 0 = nothing?

Yes. Zero is nothing.

I don't know what math peoples think of zeros. The poor had this figured out way before that mudslime declared it so.

Because that's how multiplication is defined.

You don't have to assume a field, it works in any ring.

...

[eqn]0 \cdot a=(0+0) \cdot a=0 \cdot a+0 \cdot a[/eqn]

which implies by cancellation that [math]0 \cdot a=0[/math], and similarly for the other side.

It boils down to wanting multiplication to be a homomorphism of addition in both arguments, while also having an additive identity. Those are both great for a number of reasons, but the downside is you lose structure in the multiplication operation.

Assume the following properties of a ring: there is an additive identity 0, i.e. x + 0 = 0 + x = x for all x
Every element x has an additive inverse -x such that x -x = 0
Distributive property
Associative property of addition

0x = 0x + 0
= 0x + (0x -0x) (existence of an additive inverse of 0x is guaranteed)
= (0x + 0x) -0x (associative property)
= (0 + 0)x -0x (distributive property)
= 0x -0x
= 0

Actually an interesting question, if multiplication is repeated addition, then what would adding zero zero times even mean?

this.
wtf pls explain

Its the definition of 0

giving a quantity to nothing is meaningless since at the end of the day its still jack shit

What is a convention and why is it useful?

this is the right answer

It isn't in arbitrary wheel, so try again sweetie

if 5*x = x then using laws of algebra shouldn't x/x equal to 5?

You can't make nothing more than nothing by multiplying nothing with a number higher than nothing.

Clear.

I have three fives.
I have 3 x 5
I have fifteen.
3 x 5 = 15.

I have zero nines.
I have 0 x 9.
I have zero
0 x 9 = 0

I have six zeroes.
I have 6 x 0
I have zero
6 x 0 = 0

Welcome to fucking preschool, kid.

Zero is not nothing. It is a number represented by a point
on the number line, it is the cardinality of the null set,
and it is the additive identity; whereas nothing is nothing.

he just provided a proof. What more do you want?

is this elegant or just raw?

Unfortunately, [math]0\cdot\infty[/math] is not defined, so your post incorrect.

raw

Imagine you build a tower higher and higher
and when no matter how tall you build,it doesnt seem to collapse wouldnt you assume that the foundation is sturdy enough?

>[math]\infty[/math] is a number
try again
however, it is defined in meme wheel theory
cs.swan.ac.uk/~csetzer/articles/wheel.pdf

It is a number. Not a real number, but a number nonetheless.

wolframalpha.com/input/?i=exponential fit {Pi, 4, I E}&lk=2

boy it sure looks like you assumed the existence of inverses there buddy. Probably want to clear up what sort of space we are working in first.

it's reasonable to assume that if multiplication is defined then you are working in some sort of ring.

Because we said so.

We literally just came up with it one day, this is not obtained from nature but only from the imagination of the human mind.

Every other post in this thread is just circular logic.

if you read the axioms of any system of math that involves division, and that includes an additive identity, they always say, specifically, that the additive identity has no multiplicative inverse, so you can't divide by 0 (division isn't its own operation, division is defined as multiplication by a multiplicative inverse, which requires the existence of said multiplicative inverse).

abstract algebra is a cool course and I'm happy i'm taking it

infinite nothing is nothing

using your hands, count to ten zero times

Get ready for brainlet/no mathematical aptitude response.
times = "groups of"
0*2 = 0
0 'groups of' 2 = 0
Elementary school btw
also free shkreli

>The Xbox 360, Xbox Circle? Who the fuck they think they are, they think they’re smart and shit? We ain’t doin’ geometry, we tryin’ ta play some games.

lets say we have the number 2 and try to multiply it by zero. the origin number wouldnt make sense to multiply by a phantom number so we, instead, switch our start to 0 multiplying by 2. naturally you cannot derive something out of nothing by means of doubling the nothing. that is why it is zero. this is the most rudimentary way i could explain it.

Why is dividing by 0 impossible? You're infinitely putting nothing into something and getting nothing. So, how can there be no result?

Because dividing by into "multiples" of 0 is impossible.

Dividing by 0 is multiplying by the inverse of 0, i.e. the number that you multiply by 0 to get 1. No such number exists because anything times 0 is 0.

You can divide by 0 in the trivial ring {0}. In that case 0/0 = 0.

But what makes it sturdy?

Take and think of it in the reverse.

If you have a group of 6 and you want to "divide" it into 3 groups you will get 3 groups of 2.
If you have a group of 8 and you want to "divide" it into 2 groups you will get 2 groups of 4.

How do you then take a group of N and "divide" it into 0 groups?

>why is none of something always nothing

This is a stupid maths questions thread so I'll ask my stupid maths question.

If you consider 2x to be (x + x), would you consider 6 / 2x to be the same as 3x or (x + x + x)?

If not, then why if you substitute x for (1+2) would you consider it to be 3(1+2)?

just some arbitrary rule some mathcuck made up

don't wrack your brain trying to make sense of it

I think what you meant to type there is (6/2)x=3x=x+x+x

a*3=a+a+a
a*2=a+a
a*1=a
a*0=0

I swear I know where this is

Cos if u have a number no times then you dont have a number innit

actually, i wrote this wrong
a*3=a*a*a
a*2=a*a
a*1=a
(a*0=a-a)

>i repeat nothing multiple times, that will make me sound like i know what im talking about

Guywithashrunkenhead.png

>cirkus logic

i wrote it right the first time *=/=^

Wrong
Undefined.

if any number is 5
0+0+0+0+0 = 0.

no
you