Write the first line of your proof a units high. Write the next line of your proof a/2 units high. Then, write the next line a/4 units high. Continue the pattern, writing the nth line units high. What you’re doing is mathematical reasoning, and thus you’re being rational. The set of rationals is only countably infinite, so within the infinite number of statements you make, the proof of whatever you’re trying to prove is bound to arise somewhere.

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you haven’t accounted for the spaces between the lines

That’s a trivial issue.

How so?

The spaces between the lines are proportional to the lines around them. All you have to do is account for them as well in the infinite series.

FWIW: WordPress has these built-in LaTeX tags.

http://en.support.wordpress.com/latex/

Oh whoops, I forgot that one needs to type “latex” within the dollar signs here. Thanks!

The ath line? So what’s n? 😛

what, its the nth line, but the starting width is a

Yeah, it took me quite a while before I realized what you two were referring to. Whoops. =P Corrected.