Re: Calculus XOR Probability

Tony Orlow wrote:
Matt Gutting said:
Tony Orlow wrote:
Matt Gutting said:


*My* question is, since you haven't actually defined oo, how can you tell
whether oo or 2/oo exist?

Because that's the LIMIT. You want to take the limit as n->oo?

Yes, or writing it out without shorthand, I want to take the limit as
n increases without bound.

Well, oo has to
exist, doesn't it?

Not necessarily.

Oh. Then the symbol doesn't necessarily mean anything. Can you take a limit as
n approaches soemthing that doesn't exist?

Tony, please try to be a little less dim. Or pay attention occasionally
when people tell you things. By convention, the (mathematical) limit of
a (mathematically) infinite sequence is written as:

lim[n->oo] Pn

but this "n->oo" does not mean "as n gets closer to something called
'oo'". It simply means "as n increases without limit". You have been
told this several times. This is the meaning of the symbols given to
them by the people who are writing them, so just listen to what the
authors say what they mean, or go away.

<snippino>

I'm not talking about the limit as n approaches anything, as you seem to imply
from the way you write "the limit as n->oo". I'm talking about the limit as n
increases without bound. I don't believe oo exists as a number.

Then you have no business talking about the identity between the staircase "in
the limit" and the diagonal. If oo doesn't exist, then they never are the same,
and the whole discussion goes out the window.

You have been told this before, too. Mathematics defines, very
carefully, what is meant by
"the limit of a sequence". If anyone says "in the limit", this is only
a bit of shorthand, for attentive and bright readers - I know you think
you're terribly clever, but you always need to take the very careful
statement, because your terrible cleverness otherwise causes you to
take shortcuts down wormholes that come out somewhere entirely
different.

<snip more rambling>

Brian Chandler
http://imaginatorium.org

.

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