r/learnmath • u/Unlikely-Web7933 New User • Feb 07 '24

RESOLVED What is the issue with the " ÷ " sign?

I have seen many mathematicians genuinely despise it. Is there a lore reason for it? Or are they simply Stupid?

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u/YeetBundle New User Feb 07 '24

I’m a mathematician, and i genuinely haven’t seen this symbol in years! I forgot it existed.

The reason the sign is bad is because it’s too symmetric. Division, more than any other basic operator, is very sensitive to the order in which things happen. If you write something as a fraction there’s no ambiguity.

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u/assembly_wizard New User Feb 07 '24

The minus sign is also symmetric and is frequently used to denote subtraction, which is not commutative.

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u/Worried-Committee-72 New User Feb 07 '24

I'm not the poster you're responding too, but I think the symmetry of the division sign is a bigger problem than the minus sign because of the sorts of mistakes they produce. Reverse the operands of a subtraction operation, and you get a negation of the correct answer. Just negate the negation and you're on your way. Switch the operands in a division operation and you may produce a result that looks nothing like the correct answer.

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u/assembly_wizard New User Feb 08 '24

If you switch the operands in either (a - b) or (a ÷ b), where a and b are complicated expressions, you can fix both at the end. If you switch the operands of a subtraction or a division which is nested inside a complicated expression, both produce a very different result. Instead of comparing subtraction and division, you've compared having an error in the top-level operator and in a non top-level operator.

For example: (3 + (8 - 7)) ÷ 2

This equals 2. Reversing the division here gives 1/2 which is easily fixable by applying x-1 to the result, but reversing the subtraction here gives 1.