〈 Berger | Dillon 〉

infinity is not a number

The concept of "number" is pretty flexible. Humans started with whole numbers, then included fractions, then irrational numbers, then zero, then negative numbers, then imaginary and complex numbers. The "extended reals" include +infinity and -infinity: https://en.wikipedia.org/wiki/Extended_real_number_line …

I'm a big fan of the extended reals. Perhaps i should have said "naive manipulations treated as a number are invalid", but that didn't have the same zing to it

Even that is questionable. If you want 1/infinity = 0 then you have problems, but if you think of it as infinitesimally small but non-zero, then you can generate an ordered field that extends R. In that field you're treating infinity as a number and using naive manipulations.