Equals Sign - Incorrect Usage

Incorrect Usage

The equals sign can be used incorrectly within a mathematical argument, if used in a manner that connects steps of math in a non-standard way, rather than to show equality. For example, if one were finding the sum, step by step, of the numbers 1, 2, 3, 4, and 5, one might write:

1 + 2 = 3 + 3 = 6 + 4 = 10 + 5 = 15

Structurally, this is shorthand for

( + 4 = 10) + 5 = 15

but the notation is incorrect, because each part of the equality has a different value. If interpreted strictly as it says, it implies

3 = 6 = 10 = 15 = 15

A correct version of the argument would be

1 + 2 = 3; 3 + 3 = 6; 6 + 4 = 10; 10 + 5 = 15

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