Is Full Equal to Empty?
Date: 06/15/99 at 13:03:06 From: Joseph Subject: A weird question Hi, Joseph again! I have a question I could not understand. Could you help me? thanks! 1/2 full = 1/2 empty So when we multiply both sides of the equation by 1/2, won't we get full = empty?
Date: 06/15/99 at 17:39:53 From: Doctor Rick Subject: Re: A weird question Hi, Joseph. Cute! This is just one of many examples of why we don't use English as the language of mathematics. "Half empty" does not mean "1/2 times empty." If we let full mean V (volume of a full glass) and empty mean 0 (nothing in the glass), then you would have 1/2 * V = 1/2 * 0 which is, of course, false (unless the glass can't hold anything - then V = 0). What we really mean by "half empty" is halfway from full to empty, while "half full" means halfway from empty to full. If I were to translate the phrases into math, they would be half full: 0 + 1/2 * V half empty: V - 1/2 * V These, of course, are equal. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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