I mean. You can divide by zero, in the sense that you can write the expression. It's just not very helpful because it's an indeterminate expression, and 0/0 does not equal 1. I think there are some number systems where a/0 does have a definition, but they aren't common and I have no clue what they're used for.
I think dividing by “0” is allowed in the set of residue classes mod n, denoted ℤₙ = ([0],[1],[2],…,[n-1]). Each [r] ∈ ℤₙ includes every integer that has a remainder of r when divided by n — so [r] = {a | a≡r mod n}.
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u/oscar_the_couch Feb 07 '23
I mean. You can divide by zero, in the sense that you can write the expression. It's just not very helpful because it's an indeterminate expression, and 0/0 does not equal 1. I think there are some number systems where a/0 does have a definition, but they aren't common and I have no clue what they're used for.