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Why does 13 divided by 0 not equal infinity?

Why does 13 divided by 0 not equal infinity? I really don't understand why? :confused:

My Maths teacher who has a PhD. in Mathematics told us. So basically I told my friend in another class, and she said it doesn't. So we both decided to have a bet on here on which one of us is right.

EDIT: stop repping me guys! I wanna keep my ruby's!

(edited 10 years ago)

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Reply 1

SiMan

It doesn't? pffft why wouldn't it?

Reply 2

TenOfThem

Original post by tazmaniac97

Why does 13 divided by 0 not equal infinity? I really don't understand why? :confused:

My Maths teacher who has a PhD. in Mathematics told us. So basically I told my friend in another class, and she said it doesn't. So we both decided to have a bet on here on which one of us is right.

\dfrac{n}{0}

is undefined

Reply 3

tazmaniac97

Original post by SiMan

It doesn't? pffft why wouldn't it?

Original post by TenOfThem

\dfrac{n}{0}

is undefined

but my maths teacher who has a PHD said it would, why should I believe you and not him?

Reply 4

Strangey

Original post by tazmaniac97

Why does 13 divided by 0 not equal infinity? I really don't understand why? :confused:

My Maths teacher who has a PhD. in Mathematics told us. So basically I told my friend in another class, and she said it doesn't. So we both decided to have a bet on here on which one of us is right.

n/0 is undefined; there's no answer as it doesn't make mathematical sense.

Reply 5

tazmaniac97

Original post by Strangey

n/0 is undefined; there's no answer as it doesn't make mathematical sense.

who says it doesn't make mathematical sense, it makes perfect mathematical sense to me.

Reply 6

SiMan

Original post by tazmaniac97

but my maths teacher who has a PHD said it would, why should I believe you and not him?

Well if he says cows are birds would you believe him because he is a PhD? Ask him to prove it then.

Reply 7

2710

Original post by tazmaniac97

who says it doesn't make mathematical sense, it makes perfect mathematical sense to me.

How does it make perfect sense? 0 x infinity does not give you 13.....

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Reply 8

james22

Original post by tazmaniac97

who says it doesn't make mathematical sense, it makes perfect mathematical sense to me.

The real numbers are defined as a field along with several other properties which don't matter for this. Using just the properties of a field, we can show that 0 has no multiplicitive inverse as follows-

Assume 0^(-1)=k

Then 0*k=1 (property of inverses)

so (0+0)*k=1 (0 is the additive identity)

so 0*k+0*k=1 (distributive property)

so 1+0*k=1 (by 2nd line)

so 0*k=0 (take 1 from both sides)

which is a contradiction since 0 does not equal 1.

Reply 9

james22

One thing you can sometimes do to try and get an understanding of things which aren't defined is to take limits. For example the limit as x->0 of x/x is 1, and the limit as x->0 of 1/x^2 is infinity, but the limit of 1/x as x->0 does not exist. To see this let x->0 from above (so x is always positive) and you get infinity. Also let x->0 from below, so you get -infinity. Since a limit must have only 1 value, it cannot exist in this case.

Reply 10

bluebell_flames

Original post by tazmaniac97

who says it doesn't make mathematical sense, it makes perfect mathematical sense to me.

From the age 5 up until about 15, I thought infinity made perfect 'mathematical sense' to me. And then I started to find out about the actual maths, and realised I really didn't have a clue. Don't be fooled by what seems like common sense...

Reply 11

Manitude

Original post by tazmaniac97

who says it doesn't make mathematical sense, it makes perfect mathematical sense to me.

It probably makes little mathematical sense because you don't know that much about mathematics. Sounds harsh, but in this case I'm afraid it is true. I don't claim to be especially knowledgeable, but at least I looked at the wikipedia and wolfram mathworld pages on this.

Suppose

\frac{a}{0}=\infty

This implies that

\infty \times 0 = a

where

a \neq 0

. And I really hope you can see why that doesn't make sense.

(edited 10 years ago)

Reply 12

Flauta

If you had an infinite number of nothing, you'd still have nothing, you wouldn't magically get numbers coming out of nowhere :tongue:

Therefore it's undefined

Reply 13

Felix Felicis

Original post by tazmaniac97

but my maths teacher who has a PHD said it would, why should I believe you and not him?

Do not worry, I am a professor Emeritus from Harvard in mathematics, therefore the mathematical validity of my statement supercedes that of your mathematics teacher's. :smile:

Either you are misquoting him and he said something like "as x gets really small from the RHS, 13/x tends to infinity" or he shouldn't have a PhD in maths if he makes a mistake like this.

13/0 just like 1/0, 2/0, ... , a/0 is undefined.

(edited 10 years ago)

Reply 14

Namige

What he said ^. Saying 1/0 equals infinity is like saying an infinite amount of nothing will give you something. It simply does not make sense.

Reply 15

ninuzu

There's SO many YouTube videos on dividing by zero... Numberphile actually found that it could actually equal anything you like, and they came up with a proof to show it.

Reply 16

tazmaniac97

Original post by SiMan

Well if he says cows are birds would you believe him because he is a PhD? Ask him to prove it then.

But if he said that then there must be a good reason for it, so I would believe him

Reply 17

tazmaniac97

Original post by 2710

How does it make perfect sense? 0 x infinity does not give you 13.....

Posted from TSR Mobile

Yeah but if I applied your logic to this situation, then...
13 x 0 = 0
so why doesn't 0 divided by 0 equal 13

Reply 18

Felix Felicis

Original post by tazmaniac97

Yeah but if I applied your logic to this situation, then...
13 x 0 = 0
so why doesn't 0 divided by 0 equal 13

Please read this entire wikipedia article before posting again.

Reply 19

interstitial

Original post by tazmaniac97

Why does 13 divided by 0 not equal infinity? I really don't understand why? :confused:

My Maths teacher who has a PhD. in Mathematics told us. So basically I told my friend in another class, and she said it doesn't. So we both decided to have a bet on here on which one of us is right.

Because if it did, you could make any number equal to any other. For example,

13/0=5/0 (assuming dividing by 0 gives infinity)

So multiplying by 0 would give 13=5, which is clearly false, so dividing by 0 is simply undefined.

Hope this clears it up :smile:

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