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Not quite, but close.

When you examine the limit of a function as the denominator approaches zero, it approaches infinity, but never quite reaches it.

You can see this by just taking a few examples of reducing denominators;
1/1 is 1, 1/.1 is 10, 1/.01 is 100, and so on.

(Killing time with nerdliness, hooray)

That is not technically true because you are defining infinity as a set number.
Not quite, but close.

When you examine the limit of a function as the denominator approaches zero, it approaches infinity, but never quite reaches it.

You can see this by just taking a few examples of reducing denominators;
1/1 is 1, 1/.1 is 10, 1/.01 is 100, and so on.

(Killing time with nerdliness, hooray)

That is not technically true because you are defining infinity as a set number.


I am not defining infinity as a set number.

The attempt continues ad infinitum, each time resulting in a larger and larger number (hence 'approaches infinity'). One could, purely theoretically, keep going forever naming larger and larger numbers.

The use of actual numbers was just to demonstrate the concept that as the denominator reduces towards zero, the value of the fraction increases.

Thats almost the same thing (as i understand it, dividing by zero yields multiple different types of infinity, hence undefined)


Not quite, but close.

When you examine the limit of a function as the denominator approaches zero, it approaches infinity, but never quite reaches it.

You can see this by just taking a few examples of reducing denominators;
1/1 is 1, 1/.1 is 10, 1/.01 is 100, and so on.

(Killing time with nerdliness, hooray)

Yes, yes, i know. Its approach, not equal. You get my point, dividing by a number infinitely close to zero yields multiple values which are infinitely close to multiple infinities. Negative inf, positive inf, theres a few in the imaginary numbers, etc.
I am not defining infinity as a set number.

The attempt continues ad infinitum, each time resulting in a larger and larger number (hence 'approaches infinity'). One could, purely theoretically, keep going forever naming larger and larger numbers.

The use of actual numbers was just to demonstrate the concept that as the denominator reduces towards zero, the value of the fraction increases.

01/16/2013 08:55 PMPosted by Rtsprog
it approaches infinity, but never quite reaches it.

Which means that infinity can be reached in the first place which suggests it is a set number. 1/0 is infinity is what I am getting at.
Edit the quote did not work to well I need to fix that.
[quote] 1/0 is infinity is what I am getting at.

Its more than one infinity, which is why we say undefined
Chuck Norris doesn't play Starcraft 2. He thinks about winning & then collects the trophies.
01/16/2013 09:07 PMPosted by SunnyD
Its more than one infinity, which is why we say undefined

No it is one form of infinity, there is more then one form of infinity but 1/0 is one form of it.
Which means that infinity can be reached in the first place which suggests it is a set number. 1/0 is infinity is what I am getting at.
Edit the quote did not work to well I need to fix that.


Aha, I see what you're getting at.

Approaching but never reaching doesn't imply that it can be reached - in fact, quite the opposite (that's the 'never quite reaching' part)

I could delete the 'quite' from that, and leave it 'approaching but never reaching.'

1/0 is not infinity, it's undefined.

Lim(x->0) 1/0 is infinity.
Aha, I see what you're getting at.

Approaching but never reaching doesn't imply that it can be reached - in fact, quite the opposite (that's the 'never quite reaching' part)

I could delete the 'quite' from that, and leave it 'approaching but never reaching.'

1/0 is not infinity, it's undefined.

Lim(x->0) 1/0 is infinity.

Ok I get what you are saying now but I still disagree and to try and prove my point How would you define infinity?
01/16/2013 09:09 PMPosted by Rtsprog
Its more than one infinity, which is why we say undefined

No it is one form of infinity, there is more then one form of infinity but 1/0 is one form of it.

Thats completely wrong. Take 1/x

As x approaches 0 from the positive side of the number line, x -> positive inf.
But as x -> 0 from the negative side of the number line, x -> negative inf.

Cant be one or the other, thus its both, or undefined
Thats completely wrong. Take 1/x

As x approaches 0 from the positive side of the number line, x -> positive inf.
But as x -> 0 from the negative side of the number line, x -> negative inf.

Cant be one or the other, thus its both, or undefined

How would you define infinity?
Aha, I see what you're getting at.

Approaching but never reaching doesn't imply that it can be reached - in fact, quite the opposite (that's the 'never quite reaching' part)

I could delete the 'quite' from that, and leave it 'approaching but never reaching.'

1/0 is not infinity, it's undefined.

Lim(x->0) 1/0 is infinity.

Ok I get what you are saying now but I still disagree and to try and prove my point How would you define infinity?


Infinity is a concept which stands in for an unlimited amount or number.

It's treated as a number in maths, but is not part of the set of real numbers. With relation to real numbers, it can be thought of as larger than all real numbers.

It's also the inverse of an infinitesimal, which is as close to zero as infinity is larger than all real numbers.

(It's also really useful in physics)
Infinity is a concept which stands in for an unlimited amount or number.

It's treated as a number in maths, but is not part of the set of real numbers. With relation to real numbers, it can be thought of as larger than all real numbers.

It's also the inverse of an infinitesimal, which is as close to zero as infinity is larger than all real numbers.

Ok, That description more or less fits 1/0 also when you take derivatives you assume that 1/0 = infinity.
Thats completely wrong. Take 1/x

As x approaches 0 from the positive side of the number line, x -> positive inf.
But as x -> 0 from the negative side of the number line, x -> negative inf.

Cant be one or the other, thus its both, or undefined

How would you define infinity?

I dont get what your getting at but i`ll bite

Infinity isnt a number, its the idea of a limitless value. You cant put infinity as a part of any set of reals, integers, nothing, cause it aint a number.

Ok I get what you are saying now but I still disagree and to try and prove my point How would you define infinity?


Infinity is a concept which stands in for an unlimited amount or number.

It's treated as a number in maths, but is not part of the set of real numbers. With relation to real numbers, it can be thought of as larger than all real numbers.

It's also the inverse of an infinitesimal, which is as close to zero as infinity is larger than all real numbers.

(It's also really useful in physics)

Haha you copy pasted off of wikipedia didnt you?
I dont get what your getting at but i`ll bite

Infinity isnt a number, its the idea of a limitless value. You cant put infinity as a part of any set of reals, integers, nothing, cause it aint a number.

Therefore it cannot be negative or positive because it is not a number.
Edit:you more or less are correct though.
I dont get what your getting at but i`ll bite

Infinity isnt a number, its the idea of a limitless value. You cant put infinity as a part of any set of reals, integers, nothing, cause it aint a number.

Therefore it cannot be negative or positive because it is not a number.

It mathematical terms, its often assumed to be a number, even though it is not. And the idea of infinity can be negative, theres no reason why not

I feel like you`re just playing devils advocate now
It mathematical terms, its often assumed to be a number, even though it is not. And the idea of infinity can be negative, theres no reason why not

I feel like you`re just playing devils advocate now

Lol check the edit sorry about the confusion. My entire base of argument is on proofs of derivatives.
Infinity is a concept which stands in for an unlimited amount or number.

It's treated as a number in maths, but is not part of the set of real numbers. With relation to real numbers, it can be thought of as larger than all real numbers.

It's also the inverse of an infinitesimal, which is as close to zero as infinity is larger than all real numbers.

Ok, That description more or less fits 1/0 also when you take derivatives you assume that 1/0 = infinity.


That's where you're making your mistake. It doesn't fit 1/0, it fits the limit of 1/x as 0 approaches infinity.

Derivatives are all about limits, and the limits are a necessary component.

Think about the first-principles form of the derivative;

f'(x) = lim(h->0) ((x+h)-x)/h)

It's solvable precisely because you can allow h to approach zero, removing it and any terms it's part of from the equation due to becoming infinitesimally small.
That's where you're making your mistake. It doesn't fit 1/0, it fits the limit of 1/x as 0 approaches infinity.

Derivatives are all about limits, and the limits are a necessary component.

Think about the first-principles form of the derivative;

f'(x) = lim(h->0) ((x+h)-x)/h)

It's solvable precisely because you can allow h to approach zero, removing it and any terms it's part of from the equation due to becoming infinitesimally small.

I did one proof of why e^x = e^x where i more or less ended up with infinity *1/0 = 1 I will see if I can find it but that is where I am coming from I think that you all are right though. That makes me feel like an idiot. :(

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