1 dollar = 100 cents = 10 cents * 10 cents = 1/10 dollar * 1/10 dollar = 1/100 dollar = 1 cent

Here is the proof that 1 dollar = 1 cent. Is there an error in my calculations?

Your dimensional analysis is off.

If we were talking about inches, for example, 10 in * 10 in does not = 100 in, (linear), but 100 in² or 100 sq in (planar)

likewise, 100 ¢ does not equal 10 ¢ * 10 ¢, but 10 (with no dimensional units) * 10 ¢

So instead of $1 = 100¢ = 10¢ * 10¢ = ($1)/10 * ($1)/10 = 1¢,
you get $1 = 100¢ = 10 * 10¢ = 10 * ($1)/10 = $1

Posted by TomM on 2003-05-03 04:17:16