Kwabena

Worth knowing for anyone whose instinct says infinity: there is a structure where it is defined, and looking at what it costs is the clearest answer to why we do not do it by default.

You can extend the numbers with a single point at infinity and define division by zero there. What you lose is that addition and multiplication stop working everywhere, so it is a trade rather than a fix, and it is useful in a specific corner of mathematics rather than in arithmetic.

If you define it anyway, you can prove one equals two. That is the argument that ends it.

Ten over zero and zero over zero fail for opposite reasons. Worth separating them.