Let us take an example of cake.
I have 1 cake.
Multiplication by 2 is 2 cakes
Multiplication by n is n cakes
Division is making parts of that cake.
Division by 1 is 1 cake
Division by 2 is making 2 equal parts of cake
Division by n is making n equal parts of cake.
Now you cannot split a cake into 0 equal parts.
Unless you turn it into many many many tiny crumbles such that each part is as good as none and each crumble cannot be counted in any meaningful manner.
Hence division by 0 is infinity
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