Wednesday, July 24, 2019

It may be correct to say that fractions are not numbers but are instead sentences written in a shorthand notation [COMPACTIDEA]

Fractions have intrigued me since my school days. Why are we able to represent certain values, or rather shares, precisely as fractions but not as whole numbers or decimal numbers? This can sometimes get irritating. Today a thought occurred to me which could be correct [could be wrong as well - need to think more]. Perhaps fractions aren't numbers at all. Instead, they're perhaps a quick/shorthand notation to write sentences [or instructions]. Might sound weird, but the fraction 2/3 is basically the same thing as the sentence:

Two parts out of three.

Now, the sentence - two parts out of three - definitely is not a number but is a sort of rule telling us how many parts out of how many are we talking about. A compact way to write this sentence is to write 2/3, because we've been taught from childhood that the "/" is to be interpreted as "parts out of". Just because we're all using a certain notation to write these sentences shouldn't mean we should start treating 2/3, 3/7, etc., as numbers.

Or it could very well be that due to inherent limitations of our base-10 decimal system, we aren't able to represent 1/3 precisely as a number, so we've started taking 1/3 itself as a number.

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