Infinity * 0 = ...

sikes

what does inifinity times 0 equal.

1/0 = infinity

1 = infinity * 0

surely this cant be right?

Ghost Train

according to wikipedia zero multiplied infinity is not defined, i would have thought anything multiplied by zero is zero

http://en.wikipedia.org/wiki/Infinity

Yakuza

Your logic breaks down as soon as you try to divide by zero: 1/0 isn't really "infinity", it's undefined when the divisor is zero.

As x goes to (note: goes to, never actually reaches) zero , 1/x gets larger (or "tends to infinity"). But you can't ever divide by zero, otherwise you can prove any old rubbish:
x=0, 2x = 3x.
Divide by x, 2=3. Total baloney (as you've divided by zero).

This is why the division operation is not defined when the divisor is zero.

Gah - I could have saved myself some typing by pasting this link: http://en.wikipedia.org/wiki/Division_by_zero

Hope this helps

vallo

sikes wrote:

what does inifinity times 0 equal.

1/0 = infinity

1 = infinity * 0

surely this cant be right?

Even if we could ignore the divide by zero problem (which we can't), and allowed that 1/0 was infinity (which it isn't) there is still another error.
You started with
1/0 = infinity

To get to you the next line, you have to multiply both sides of the equation by 0 which would give

(0*1)/0 = 0 * infinity
which leads to
0 = 0 * infinity
or
0 = 0

breadmonkey

As has been said,

1/0 ≠ ∞

nothing

That and zero is a place marker and not an actual number.... I knew History of Maths wasn't a totally useless subject... Ok I didn't, but I do now!

ecksor

If you want to go multiplying by something called "infinity" you have to actually consider what set of objects contains this "infinity" object and how you're defining multiplication. None of the commonly used number systems contains it.

mathias

Infinity is not a number , its a concept , there are an infinity of infinities on the number line , between any two integers there is an infinity of infinities !!

sikes

cheers for the replies.

To get to you the next line, you have to multiply both sides of the equation by 0 which would give

(0*1)/0 = 0 * infinity
which leads to
0 = 0 * infinity
or
0 = 0

you conviently but brackets in the first line, without them, the maths in my orginal equation is right, regardless of the value of infinity!

(0)(1/0) = 0 * Infinity


----

basically what i was trying to figure out was.

You have 2 people with coats. Person A never has a black coat. Person B has an infintely greater chance than A of having a black coat.

How chance has B of a Black coat?

kind of stupid example but hope you get my drift

Son Goku

sikes wrote:

what does inifinity times 0 equal.

1/0 = infinity

1 = infinity * 0

surely this cant be right?

As has already been said 1/0 is not infinity it is undefined. However you've actually come across the reason why it is undefined yourself.

Since 1/3 * 3 = 1, 1/4 * 4 = 1 and so on, we see most numbers have a muliplicative inverse.

However using this logic we would get 1/0 * 0 = 1, which as you said can't be right, because multiplication by 0 is defined to equal 0. So by allowing division to operate on 0 we've reached a contradiction.

You can either resolve this in two ways:
(a)Say you won't allow division by 0 in your number system, that it is undefined.
(b)Make a number system where it is defined. However these systems have really complicated rules making them almost completely unworkable. Also the natural world is modelled better by number systems where division by 0 is left undefined.

im_invisible

eh, would it be right to say that the limit of x by y, as x tends to infinity and y tends to zero, is 1

(ive been up too long, im going to bed)

breadmonkey

im_invisible wrote:

eh, would it be right to say that the limit of x by y, as x tends to infinity and y tends to zero, is 1

(ive been up too long, im going to bed)

I don;t think so since you would be almost multiplying by 0??? That's abit too headwrecking for me at the moment though,zzzzZZZZzzzZZZZZZZZ

Farouk.Bulsara

im_invisible wrote:

eh, would it be right to say that the limit of x by y, as x tends to infinity and y tends to zero, is 1

(ive been up too long, im going to bed)

The answer is - it all depends!

Let's say we have two functions, both functions of some parameter, t.

f(t) = t
g(t) = 1/t

It should be obvious that as t approaches 0, f(t) approaches 0 and g(t) approaches infinity. Now look at the product:

f(t) * g(t) = t * 1/t = 1.

So the limit as t approaches 0 is equal to 1. So far, so good!

Now let's consider a variation on the above:

f(t) = t^2 (t squared)
g(t) = 1/t

=> f(t) * g(t) = t^2 * 1/t = t

So the limit of f(t) * g(t) as t approaches 0 is equal to 0.

Another case:

f(t) = t
g(t) = 1 / t^2

=> f(t) * g(t) = t * 1 / t^2 = 1 / t

So the limit in this case (as t approaches 0) is equal to infinity (or rather, the limit does not exist).

In all three cases above, we have two functions, one of which tends to zero, the other tends to infinity (as you originally asked) but we get three different limits. In fact, we can easily pick our functions to get any number we desire, or no limit at all.

So, the moral of this story is - it depends on how the two functions behave relative to each other.

Fred

Emoocrap

Hello my name is Trevor and I am 15, i joined this forum solely to reply to this hahah, well think about this.

What is infinity? It is a word and symbol attached to everything.

What is 0? It is a number, and word attached to nothing.

Now imagine a jar, this jar has infinity in it. Everything is inside it, so what is on the outside? 0.

So you might wonder where this is going. Well...if there is nothing on the outside and everything on the inside, there is a -/+ relationship between the two. Infinity is equal and opposite to 0. You guys are saying, +/- = +, there are no values attached, you could i suppose, you could attach a value to it to make it simple, 1/-1 and it is equal to 0 or in our case, -. in the beginning, before anything, there has to be nothing, or 0. so how can you think that if you have infinity, everything, and divide it by 0, nothing, that you will get everything?

JC 2K3

Emoocrap wrote:

Now imagine a jar, this jar has infinity in it. Everything is inside it, so what is on the outside? 0.

If infinity is inside the jar then what is the jar?

Tar.Aldarion

A 1 dimensional enclosure.

JC 2K3

Explain a "jar" in one dimension.

jar
–noun
1. a broad-mouthed container, usually cylindrical and of glass or earthenware: a cookie jar.

Emoocrap

the jar is a tool to help you understand the concept, the jar represents the distance that is between the two, to set a boundary between 0 and infinity, where in actuality there is only a distance in time, not a physical distance.

Farouk.Bulsara

Emoocrap wrote:

Hello my name is Trevor and I am 15, i joined this forum solely to reply to this hahah, well think about this.......

Trevor,

This forum is for discussing mathematics. I suspect that you are in the wrong place. Have you tried looking for a forum that caters for immature 15 year-old boys?

Fred :rolleyes:

Tar.Aldarion

How does he come accross as immature? Cop on.

oRlyYaRly

Farouk.Bulsara wrote:

Trevor,

This forum is for discussing mathematics. I suspect that you are in the wrong place. Have you tried looking for a forum that caters for immature 15 year-old boys?

Fred :rolleyes:

Oh the irony!

JC 2K3

I like to think that anything divided or multiplied by zero or infinity is equal to zero and infinity, in the same way that root4 can be 2 or -2.

Son Goku

Emoocrap, infinity is defined formally in mathematics and has several different meanings depending on what context you use it in. Not only that, but the infinities in these contexts aren't the same "object".

There is several different infinities from set theory, an two major infinities from analysis and an infinity from algebra.

In the real numbers there is no such number as infinity, 1/0 being undefined.
Infinity usually means increasing without bound when used in mathematics. In this sense infinity is a procedure
As such division by infinity is no more meaningful than division by the integral sign.

Emoocrap

ohhhhh ok, sry bout that then hahaa, but to that person who called me immature, i think you yourself are quite immature for picking on me, when, i only tried to explain my pov and the reason i posted it here, was to recieve a much more intelligent reply. IF you havent noticed, this is not hte subject that is common among my kin. They find it boring, so the only place i can get into an engaged conversation is with 20-50yr old people. And what i was saying anyways is that 0 and infinity cant be defined. they just cant. because infinity is everything, it is absolute zero aswell. that means that 0 is infinity just the same. So, if you attempt to place a definition, you will either go mad contemplating the definition, or come up with something irrational, or, something that yet does not truly define it.

Emoocrap

OH and if you really cared that much to attempt to injure my feelings, why dont you look where else i have posted it haha, the coockus nest, and in philosophy, but it is in the aspect of a life theory, that is not mathematically rejectable,nor mathematically based, because the beginning is currently undefined,and te attempt to will destroy you. though i suppose you could reject it regardless, it was created to help kids that have motivational issues due to the bewilderment of life, and why they are in it, it pertains to the kids who want an answer to why they are here.(though it would only work on the kids who are open enough to accept it. and in our world today, it is a rare occurrence so...) Well. i wou ill leave smarties to your math conversation, i dont really belong here. i am not that math smart, only three years ahead of my grade level, and that puts me in pre-calculus. so sry

Tar.Aldarion

Yes, how dare you be pre-calculus, you ninny!

Even if what you say is wrong, it is good to post your ideas and you will learn why they are wrong, and maybe can hypothesize something else.

Emoocrap

ya go read my other post this post here came from my find in that one. it is a theory on life, and how it all began. it is correct though you cant PROVE it wrong lol its a twist but it really is correct no kidding, just read it with an open mind please.

cast_iron

You appear both mature in some respects and immature in others. What makes you think anyone here gives a toss where else you post...

Emoocrap

i dont. i am inviting them to read it, because the reason i posted here was to have it read, respectfully, you dont even have to read it, hence "invited", as in, you can REJECT. Not to be mocked and insulted, especially not by people who are like 30 years old. thank you very much. you have dropped to a level of maturity that is expected from me. thank you. i feel i am amongst my kin now. OH and somebody does care. if you read the whole thread, you would have noticed it, he said i should go find a board for immature little 15 year olds. and i came back with, i did. OBVIOUSLY, if he cared enough to post it, he wouldnt mind me telling him i have found a board that is way better suited than here, for my statement. and i apologized for posting here. my statement was out of context. but again, thank you for trying to belittle me.

ecksor

Ok, of all the forums this should be the last one where age matters. Either the arguments are logical and convincing or they're not ...

Anyway, let's just try to stick to the maths and get away from the personal snipes.

Farouk.Bulsara

Emoocrap wrote:

i dont. i am inviting them to read it, because the reason i posted here was to have it read, respectfully, .... Not to be mocked and insulted, especially not by people who are like 30 years old. thank you very much....(etc)

Trevor,

You began your first post on this forum with the words "you all are silly". Silliness is associated with immaturity.

Can you explain why it is OK for you to begin by insulting *everyone* on this forum, but apparently not OK for anyone here to question *your* maturity?

If you have time, perhaps you might also explain how you think that you will get the respect that you are looking for from anyone with such an attitude?

Fred

Emoocrap

Farouk.Bulsara wrote:

Trevor,

You began your first post on this forum with the words "you all are silly". Silliness is associated with immaturity.

Can you explain why it is OK for you to begin by insulting *everyone* on this forum, but apparently not OK for anyone here to question *your* maturity?

If you have time, perhaps you might also explain how you think that you will get the respect that you are looking for from anyone with such an attitude?

Fred

first off, you are correct. I apologize. my bad.

But maturity, is not set in stone. There is no set standard for maturity, it is a point of view relative term. but my word choice does not warrant your behavior either. i could have said stupid or dumb just the same, so what silly is viewed as, should not matter. I also never said it was not ok for you to question my maturity, as you should seeing as i am 15. and i thank you for analizing it but i would rathere it wasnt so inclined towards being spiteful

Farouk.Bulsara

Emoocrap wrote:

first off, you are correct. I apologize. my bad.

But maturity, is not set in stone. There is no set standard for maturity, it is a point of view relative term. but my word choice does not warrant your behavior either. i could have said stupid or dumb just the same, so what silly is viewed as, should not matter. I also never said it was not ok for you to question my maturity, as you should seeing as i am 15. and i thank you for analizing it but i would rathere it wasnt so inclined towards being spiteful

Trevor,

Thanks. And apologies accepted. I am still a bit confused by your response though ... you say that you could have said "stupid" or "dumb" ... how exactly do you expect to get respect or get people to take you seriously if you begin your communication by calling everyone "silly", "stupid" or "dumb"? That still doesn't make much sense to me.

I was not being spiteful - if you thought so, then please accept my apologies.

Fred

Farouk.Bulsara

JC 2K3 wrote:

I like to think that anything divided or multiplied by zero or infinity is equal to zero and infinity, in the same way that root4 can be 2 or -2.

Hi JC2K3,

Dividing "anything" by zero is generally thought to be not good, and dividing zero by zero is generally accepted as not defined. A lot of these problems can be solved using limits (and other methods). For example, sin(x) divided by x is not defined if x is equal to 0, but it can be shown that the limit of sin(x) / x is actually equal to 1.

Here's another one to think about:

If we raise a positive number (greater than 1) to a power of a positive integer (greater than 1), we get a number greater than the original number, right? For example, raising 2 to the power of 5 gives 32.

So, what do we get if we raise (1 + 1/n) to the power of n, as n tends to infinity?

Clearly, the "1 + 1/n" term is greater than 1, so raising it to the power of a large number should give an even larger number. And as n tends towards infinity, what do we get?

Fred

Emoocrap

haha, i do, of course accept your apology, and i actually did not mean to put that there, hahhaahahaha, i did, but then i revised it after i posted and realized it was belittling everybody in here, and i tried to erase it, but i couldn't find out how, seeing as it was my first post and all...so i left it.

anyways, sry bout all that. now i have another huge mess to deal with over in the cuckoo and philosophy forums : / everybody seems to think i am just a 15 yr old kid on drugs, i get ABSOLUTELY no respect from them. hahaha. though i am holding VERY large claims... i think i found the answer to life, and how we started. no joke. i am again inviting you to read it i would like your input. you seem a lot more level headed then them... and a lot more mature. i only ask that you do not include the fact that i have EXPERIMINTED with psychedelics, in your reply. it seems that everybody thinks i am crazy and need help because of it, i am not addicted. they don't form addiction. but anyways, if you don't want to,


thank you for helping clear this all up,

no hard feelings,
Trevor

JC 2K3

Farouk.Bulsara wrote:

Clearly, the "1 + 1/n" term is greater than 1, so raising it to the power of a large number should give an even larger number. And as n tends towards infinity, what do we get?

Oh, but it is one.

You see infinity is the very last term before the loop starts again. The infinity-ith term is the same as U0. You can either go back one to U0 and get 1(anything to the power of 0 is 1) or go infinitely forward to the last term before U1 occurs again.

Farouk.Bulsara

JC 2K3 wrote:

Oh, but it is one.

You see infinity is the very last term before the loop starts again. The infinity-ith term is the same as U0. You can either go back one to U0 and get 1(anything to the power of 0 is 1) or go infinitely forward to the last term before U1 occurs again.

Hi JC2K3,

Gosh! One infinity is enough before even thinking of looping again!

When we apply our intuition to this problem, there are two approaches.

The first approach says: "1 + 1/n" approaches 1 as n tends to infinity. And 1 to the power of n, no matter how large n is, is equal to 1.

The other approach says: "1 + 1/n" is always greater than 1, no matter how small 1/n is. Hence raising any number greater than 1 to an ever increasing power should result in an ever increasing result. In other words, the limit is unbounded - i.e. infinity.

However, neither approach is correct. The actual answer is somewhere in between! In fact, as n gets larger and larger, the term (1 + 1/n)^n gets closer and closer to 2.718...

You can validate this yourself on a calculator:

1.01 ^ 100 = 2.7048...
1.001 ^ 1000 = 2.7169...
1.0001 ^ 10000 = 2.7181...

By the way, the number that you get (2.718...) is Euler's Constant and is given a special letter: e.

Fred

JC 2K3

Oh yeah... I knew that..... Thought I'd be all smart and come up with something that seemed smart

Farouk.Bulsara

JC 2K3 wrote:

Oh yeah... I knew that..... Thought I'd be all smart and come up with something that seemed smart

Hi JC 2K3,

hahaha, lol, , hahaha, hehehe, lol,

that was real smart

Fred