O/T - How many kinds of infinity are there? [Helps if you're a Maths geek]

Goldstone1976

We Got Calde in!!

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Apr 30, 2013

13,788

Herts

• Jun 8, 2014

• #1

I came across this from a Brian Cox tweet: https://www.youtube.com/watch?v=23I5GS4JiDg

It's long (at 15 minutes), but thoroughly entertaining if you have (more than?) a passing interest in number theory. Sur Complex numbers, anyone?

 

Triggaaar

Well-known member

Oct 24, 2005

50,201

Goldstone

• Jun 8, 2014

• #2

We've had a thread on this before. Some geeky idiot on numberwang (or something like that) argued that some infinities are bigger than others. He was wrong, of course.

 

Goldstone1976

We Got Calde in!!

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Apr 30, 2013

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Herts

• Jun 8, 2014

• Thread starter
• #3

Triggaaar said:

We've had a thread on this before. Some geeky idiot on numberwang (or something like that) argued that some infinities are bigger than others. He was wrong, of course.

Click to expand...

Ooops; sorry. Normally, I do a search on NSC before starting a new thread to see if anything has been posted on it previously before starting mine. I didn't bother on this occasion because...well, because I really didn't think there would be. Never underestimate NSC is the moral of that snippet.

Oh, btw, he was right of course. But you knew that and wanted to start a binfest. I'm game!

 

Triggaaar

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Oct 24, 2005

50,201

Goldstone

• Jun 8, 2014

• #4

Goldstone1976 said:

Ooops; sorry.

Click to expand...

Nothing to apologise for. I've never seen that video before, and just because there's been a thread on infinity doesn't mean we can never have another.

Oh, btw, he was right of course.

Click to expand...

If he was right, and you explained it to me, I'm probably too stupid to understand. I'm just gonna stick with disagreeing.

 

Triggaaar

Well-known member

Oct 24, 2005

50,201

Goldstone

• Jun 8, 2014

• #5

This was his argument: One type of infinity is
1, 2, 3, 4, 5 ...
Another type is
1/1, 1/2, 1/3, 1/4 ...
But in that second example, the numerator never changes. So you can list different infinities like so:
1/1, 1/2, 1/3, 1/4 ...
2/1, 2/2, 2/3, 2/4 ...
3/1, 3/2, 3/3, 3/4 ...
4/1, 4/2, 4/3, 4/4 ...

and a different type of infinity would be to include them all, by counting diagonally, instead of horizontally, as follows:
1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4 ...

He claimed that that infinity was bigger than the others. I disagree.

 

Everest

Me

Jul 5, 2003

20,741

Southwick

• Jun 8, 2014

• #6

Triggaaar said:

We've had a thread on this before.

Click to expand...

You can never have enough threads about infinity

 

Kosh

'The' Yaztromo

Jul 14, 2003

5,219

Yaztromo's Tower; the borders of Darkwood Forest

• Jun 8, 2014

• #7

Ernest demonstrates clear understanding in relation to this theory, after all he's discovered an infinite number of possibilities when it comes to using the same "joke" since time immemorial.

Kosh

 

Goldstone1976

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• #8

Triggaaar said:

This was his argument: One type of infinity is
1, 2, 3, 4, 5 ...
Another type is
1/1, 1/2, 1/3, 1/4 ...
But in that second example, the numerator never changes. So you can list different infinities like so:
1/1, 1/2, 1/3, 1/4 ...
2/1, 2/2, 2/3, 2/4 ...
3/1, 3/2, 3/3, 3/4 ...
4/1, 4/2, 4/3, 4/4 ...

and a different type of infinity would be to include them all, by counting diagonally, instead of horizontally, as follows:
1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4 ...

He claimed that that infinity was bigger than the others. I disagree.

Click to expand...

That's a classic way of showing it. There tend to be two main issues with folk struggling to get their heads around the problem:

1) Minor issue: The definition of "bigger". Infinities are described in terms of the length of the series or how close you can get to a predetermined "real" number, typically 1, without actually reaching it.

2) Major issue: The definition of "infinity". The lay person's definition is only one (of several score) definition and does not preclude there being other infinities.

I need to leave now for a few hours - if you'd like a non-mathematical analogy, I can give you one (ooh, er) when I get back. There are also other simpler examples. You could do worse than watch the first couple of minutes of the video too...

EDIT: The example he cites are a "countable" infinity and an "uncountable" infinity. You could look up those terms, or I could explain on my return. Or, I could just get a life, I guess.