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Why can't you divide by zero? - Coggle Diagram
Why can't you divide by zero?
(
misconception
) isn't the answer to 10/0 infinity?
if you divide by numbers that keep shrinking to 0, the answer will grow to the largest thing possible
10 divided by a number that tends towards 0, the answer tends towards infinity
it's not the same thing as 10/0=∞
what division really means
dividing by a number is essentially the reverse of multiplying it
10/2="how many times ad 2 together to make 10" or "2 times what equals 10"
if we want to divide by 0, we need to find its multiplicative inverse, which should be 1/0 (one over zero)
what is a multiplicative inverse?
the product of any number and its multiplicative inverse is always 1
the multiplicative inverse of 2 is 1/2
this would have to be such a number that multiplying it by 0 would give 1
but since anything multiplied by 0 is still 0
such a number is impossible, so 0 has no multiplicative inverse
does that really settle things, though?
if mathematicians can create the square root of -1 as a new number called "i", couldn't we just make up a new rule, say, that ∞ means 1/0?
let's try it: imagine we don't know anything about ∞ already, based on the definition of a multiplicative inverse, 0*∞must = 1
we can make the following reasoning: (0x∞)+(0x∞)=1+1=2, (0+0)x∞=2, but (0+0)is0, that makes 0x∞=2
unfortunately, we already defined this as equal to 1, while the other side of the equation is still telling us it's equal to 2
so 0x∞=1, 0x∞=2,
1 = 2
if 1, 2, and every other number were = 0, but having ∞=0, is ultimately not all that useful to mathematicians, or anyone else
(calls for action)
BUT THAT SHOULDN'T STOP US FROM LIVING DANGEROUSLY, TO SEE IF WE CAN FUN, NEW WORDS TO EXPLORE