[Micky76]

(Original post by raheem94)
I can't say much about it.

Read this.

I have read it before. From the proofs there that I understand, they all seem to omit 1/infinity. I have thought about this before, it just leads me to the concept of some infinities being smaller or greater than other infinities. Ill explain mathematically;





In general,



Just my thoughts, I have far to little knowledge to go into this idea, Cantor spent a lifetime on it and didn't find it. But anyways, up for another debate today about this?

[raheem94]

(Original post by Micky76)
I have read it before. From the proofs there that I understand, they all seem to omit 1/infinity. I have thought about this before, it just leads me to the concept of some infinities being smaller or greater than other infinities. Ill explain mathematically;





In general,



Just my thoughts, I have far to little knowledge to go into this idea, Cantor spent a lifetime on it and didn't find it. But anyways, up for another debate today about this?

I will need to think about it.

Yeah you look likely to stir another debate today, Hasufel may like to join in

[wanderlust.xx]

(Original post by Micky76)
I have read it before. From the proofs there that I understand, they all seem to omit 1/infinity. I have thought about this before, it just leads me to the concept of some infinities being smaller or greater than other infinities. Ill explain mathematically;





In general,



Just my thoughts, I have far to little knowledge to go into this idea, Cantor spent a lifetime on it and didn't find it. But anyways, up for another debate today about this?

This is seriously shoddy. is a concept rather than an actual, physical number. Thus using it in fractions or elementary equations just isn't right.

I really dislike this about incompetent teachers. To make their life easier, when teaching division, they should tell you that one over a large number is a really small number, and one over a small number is a large number.

Instead, they use the concept of infinity, slap them in a fraction and say, 'here you go, this holds true all the time because one over infinity is zero'.

[sputum]

(Original post by Micky76)
I have read it before. From the proofs there that I understand, they all seem to omit 1/infinity.

If 1.9999... and 2 are not the same number there will be a number between them and the euclidean distance between them will be non-zero.
Demonstrating either of those would work but either your 1/inf is zero or it is not. You can pick

[DarkWhite]

(Original post by TLHroolz)
Explain:

a=b
a^2=ab
2a^2=a^2+ab
2a^2-2ab=a^2-ab
2(a^2-ab)=(a^2-ab)
2=1
?????


This was posted from The Student Room's iPhone/iPad App

(1) a=b
(2) a²=ab
(3) 2a²=a²+ab
(4) 2a²-2ab=a²-ab
(5) 2(a²-ab)=(a²-ab)
---
This is where things go crazy!
Using (2):
(6) 2(a²-a²) = (a²-a²)
(7) 2(0) = (0)
You can't divide the (0) out because dividing by zero is undefined.

Forgot I can use TeX on here, oh well.

Rule of thumb: Reduce before dividing out.

[Intriguing Alias]

Saw the title... Facepalmed.

[Slumpy]

(Original post by Micky76)
I know that is widely accepted but I just can't see it that way. Wouldn't it be true saying:



That's just my thought. But then again, the infinity fraction tends to zero... However that doesn't mean it shouldn't be there.

No.
is essentially meaningless. You can take the limit of 1/n as n goes to infinity though.
It is true that 1.9..9(it is important there is an end)=2-1/10^n, for some n, but in the limit, we get 1.9.. on the left, and 2 on the right.

[james22]

(Original post by Micky76)
I have read it before. From the proofs there that I understand, they all seem to omit 1/infinity. I have thought about this before, it just leads me to the concept of some infinities being smaller or greater than other infinities. Ill explain mathematically;





In general,



Just my thoughts, I have far to little knowledge to go into this idea, Cantor spent a lifetime on it and didn't find it. But anyways, up for another debate today about this?

If by 1/infinity you meant the limit as n_>infinity of 1/n then this=0

[Micky76]

(Original post by james22)
If by 1/infinity you meant the limit as n_>infinity of 1/n then this=0

(Original post by Slumpy)
No.
is essentially meaningless. You can take the limit of 1/n as n goes to infinity though.
It is true that 1.9..9(it is important there is an end)=2-1/10^n, for some n, but in the limit, we get 1.9.. on the left, and 2 on the right.

I understand that the limit of is zero. That doesn't mean that and hence I question why it is neglected.

[Maths_Lover]

(Original post by hassi94)
Saw the title... Facepalmed.

This.

People should know by now that if they've managed to "prove" something so non-sensical, that they've done something illegal in maths, like divided by zero.

[james22]

(Original post by Micky76)
I understand that the limit of is zero. That doesn't mean that and hence I question why it is neglected.

1/infinity is meaningless. Infinity is not a real number and since division is an operation on the real numbers (and complex but infinity isn't in them either) using division with infinity is like doing the vecor cross product of 7 and 3, it makes no sense.

[Slumpy]

(Original post by Micky76)
I understand that the limit of is zero. That doesn't mean that and hence I question why it is neglected.

Well, no.
The limit of isn't 0, because it's (at best) shorthand for something else. That is, the limit of 1/n as n tends to infinity. If we take it as this (the only sensible interpretation really), it's obviously 0. My guess is you've likely not done any sort of course on limits?

[Micky76]

(Original post by Slumpy)
Well, no.
The limit of isn't 0, because it's (at best) shorthand for something else. That is, the limit of 1/n as n tends to infinity. If we take it as this (the only sensible interpretation really), it's obviously 0. My guess is you've likely not done any sort of course on limits?

Nope I haven't. I see now how what you say works as n tends to infinity. Does that mean that similarly to division by zero, division by infinity is not "allowed"?

[Intriguing Alias]

(Original post by Micky76)
Nope I haven't. I see now how what you say works as n tends to infinity. Does that mean that similarly to division by zero, division by infinity is not "allowed"?

A little different, as you can't use infinity as a number at all, not just division. You can neither 'multiply by infinity' nor 'add infinity' etc.

[EEngWillow]

I thought it had been a few weeks since one of these threads had been posted...

Here's a semi-related fact...

[Tootles]

(Original post by TLHroolz)
Explain:

a=b
a^2=ab
2a^2=a^2+ab
2a^2-2ab=a^2-ab
2(a^2-ab)=(a^2-ab)
2=1
?????


This was posted from The Student Room's iPhone/iPad App

If memory serves, this works via division by zero and is therefore fallacious.

[Intriguing Alias]

(Original post by EEngWillow)
I thought it had been a few weeks since one of these threads had been posted...

Here's a semi-related fact...

Buh buh buh

[aznkid66]

(Original post by Micky76)
I have read it before. From the proofs there that I understand, they all seem to omit 1/infinity. I have thought about this before, it just leads me to the concept of some infinities being smaller or greater than other infinities. Ill explain mathematically;





In general,



Just my thoughts, I have far to little knowledge to go into this idea, Cantor spent a lifetime on it and didn't find it. But anyways, up for another debate today about this?

So, by your formula, ? Proof by contradiction says there is something wrong.

Here's the thing: . No one is omitting the infinitesimal because it is simply not there; the difference between 0.999... and 1 is 0.

Since multiplying by 9 or multiplying by 3 doesn't satisfy you, let's try something different.

If you subtract 0.999... from 1, what do you get? You get 0.000...1, or an infinite number of zeroes followed by a single 1, a symbol for the smallest unit possible.

It's almost like each 9 is filling up part of the 1.000..., but it doesn't quite reach it. You know what this reminds me of? Sums of infinite geometric series.

Spoiler:

Show

To summarize, it's "neglected" because it does not exist.

[EEngWillow]

(Original post by hassi94)
Buh buh buh

Oh dear, we've broken Euler.

[Micky76]

(Original post by aznkid66)
So, by your formula, ? Proof by contradiction says there is something wrong.

Yes but my initial assumption is that which doesn't completely disprove my formula. However, as hassi stated that it cant be directly used as a number has clarified things a bit. Impressive animation, I do agree with how you stated that there is no last row, so in this example, technically there is no 'last' 1 in 0.00....01 as it is at infinity. Just help infinity get up, it will be an eight :P.