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June 20th

June 20th

# Powers

## Is a × a × a = 3 a ? Is a 3 = a × 3?

Or, should we guess what is?

In mathematics, each symbol, (e.g. a ×3, 3a , a 3 ) has a uniquely defined meaning. a × 3 has been arbitrarily chosen as shorthand for a + a + a . It cannot mean anything else!

a 3 has been, equally arbitrarily, chosen as shorthand for a × a × a. It means precisely this.

3 × a is shorthand for 3a, but note that the omission of the × sign is possible only between a number and a letter (and only in that order). Omitting it from any other combination would lead to something different from a product, e.g. 33 is not 3 × 3 ; aa or a3 means a single variable consisting of two symbols each.

Always consider the (unique!) meaning of the maths you write.

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