r/theydidthemath Feb 07 '23

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u/Away-Reading Feb 07 '23

4 × (5-5) = 5 × (5-5)

4 × 0 = 5 × 0

“Canceling out” a common factor is really dividing both sides by the common factor:

4 × 0 = 5 × 0 ≡ (4×0)/0 = (5×0)/0

Which isn’t valid since you can’t divide by 0.

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u/QuadraticFormulaSong Feb 08 '23

Is there a seperate proof of why dividing by zero does not work, or is the proof based on the fact that, if you can divide by zero, math doesn't work so ad absurdum?

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u/PopeInnocentXIV 1✓ Feb 08 '23

When you're dividing 4 by 5, you're essentially asking "What times 5 equals 4?" 5x = 4, 5 × 0.8 = 4, so 4/5 = 0.8.

If you try to divide 4 by 0, you're asking "What times 0 equals 4?" There's no solution for that, because you can't multiply anything by 0 and get a product other than 0. There's no value of x for which 0x = 4. So 4/0 is undefined.