Just out of curiousity, would you define infinity as odd, even, neither, or both? I had a discussion with a friend the other day which brought up this question, and just wanted some different points of view on it. Thanks.

"Infinity [noun] - the state of having no bounds or limits, endless. [math] an indefinite number of."

This is the dictionary evrsion of infinty. Simple logic dictates that infinity is an undefined number, because if it was defined we would know what it is and it would be finite. So, because we don't know what it is (it is indeed endless) it is neither odd nor even.

It is most definitely not both odd and even, these are two mutually exclusive descriptions.

I'm not sure about your last line Chris, since every even number is of the form 2m and odd is of the form of 2m+1.

2¥ = ¥

2¥+1=¥

I agree though, infinity is not a number but a state, so it can neither be even nor odd...

Yatir

I've got a funny story relating to this, a friend of mine a few weeks ago asked me what the highest number description is, in his words "e.g million, billion, trillion - y'know..". I uttered "well a suppose that'd be a googolplex", to that his responce was "oh, so a googolplex plus one is infinity then?".

The moral to that story is obviously itemised by Yatir's post: "INFINITY IS NOT A NUMBER".
Think of infinity as being a description, "4 is an even number", "13 is a prime", and similarly "1 divided by zero is infinity"
i.e. infinity describes a number really really really (insert extra 'reallys' here) big..

Julian

There's an amusing paradox called Thompson's lamp which relates to this discussion. Suppose I have a lamp where if I switch it on now, it will stay on for half a minute, go off for a quarter of a minute, come back on again for an eighth of a minute and so on.
In 1 minute's time, is it on or off?

In effect, this amounts to asking whether or not infinity is even; it has switched from on to off or vice versa infinitely many times. Of course there is no sensible answer, except to say that you couldn't possibly construct such a lamp.

David