This is why mathematicians are so meticulous with their "if and only if", "everywhere except a countable number of points", infinimum/supremum[1] and so on, and

This is why mathematicians are so meticulous with their "if and only if", "everywhere except a countable number of points", infinimum/supremum[1] and so on, and of course equations to really nail things down. [1]: https://en.wikipedia.org/wiki/Infimum_and_supremum https://en.wikipedia.org/wiki/Infimum_and_supremum