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> Division is multiplication of a fractional value

Thus, division by 0 is multiplying by (1/0). Does such a fraction exist? It can go along two potentially different paths depending on the limit we take.

Alternatively, there is information lost when you multiply something by 0: a x 0 = 0, b x 0 = 0. When you perform an inverse by dividing, will you get back a or b (or any number)? Thus, it is not invertible at least at 0.

Disclaimer: Not a mathematician

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>Alternatively, there is information lost when you multiply something by 0: a x 0 = 0, b x 0 = 0. When you perform an inverse by dividing, will you get back a or b (or any number)? Thus, it is not invertible at least at 0.

>>A field is not strictly definitely by addition and multiplication, it is definitely by two operators where one is an abelian group (addition in our case) and the other forms and abelian group over the non identity term of the first (eg multiplication is an abelian group over non zero terms).

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