The "middle" of an infinite set

[mmm4444bot]

Continuing the discussion.

I understand that zero is not the absolute midpoint of the Real number line because infinity is weird.

Another question: Is it incorrect to claim that zero is the mean of the set of Integers?

 

[tutor_joel]

the mean of an infinite series would be undefined since you would be left with...

\(\displaystyle \frac{\infty}{\infty}\: or \:\frac{0}{\infty}\)

which doesn't really make sense eh?

Actually, it would be:

\(\displaystyle \frac{\infty - \infty}{\infty}\)

 

[mmm4444bot]

Good grief!

I must be over-enjoying my wine. I can't believe that I unwittingly tried to do arithmetic with Infinity!

That's sloppiness.

(ha, ha, ha, ha, ha, heh, heh)

(hoo boy)

Darn that Infinity.

 

[mmm4444bot]

And Glenn just warned me today about that trap (via Cantor). How embarrasing.

(Maybe he will delete this thead for me, if I ask.)

 

[tutor_joel]

I remember that it blew everyone's mind in calc when it's demonstrated that you can have an infinite series in a finite space