How many iterations are there in a dead loop?
while (true) { print('Lionel Richie - Hello'); }
One can say “There’s an infinite number of them.” And that’s true but that merely tells us that the number of iterations is greater than one (and there isn’t one such number), it does not give us an exact number. Hence, it’s not really an answer.
Since the loop literally never ends, the number of iterations is greater than EVERY number, and since there is only one such number, that is the answer to our question. I call this number “largest impossible” where by “impossible” I mean “any number larger than the largest number” and by “largest number” I mean “a number larger than every other number”.
Let that be an introduction to a thread that is entirely about controversial concepts in mathematics that people seem to love so much (and that they tend to discuss in inappropriate places.)
Let me introduce some.
Infinity refers to any number larger than every integer. There isn’t one such number but many of them.
Smallest possible infinity refers to the smallest number larger than every integer. It’s an instance of infinity and there’s only one such number.
Largest number is a number larger than every other number. It’s an instance of infinity and there’s only one such number.
Standard infinity refers to some arbitrarily chosen infinite number that can be added to, subtracted from, multiplied and divided in order to get some other infinite number (hence, it must be greater than the smallest infinity and smaller than the largest number.) The purpose of this number is to serve as some kind of standard for doing arithmetic.
Impossible number is any number larger than the largest number. I call it impossible because it’s an obvious contradiction. How can a number be larger than the largest number? It can’t. Nonetheless, contradictory concepts can be useful (in their own limited way) so we’re going to keep it.
Largest impossible is a number larger than every number. It’s similar to the largest number, but unlike the largest number, this number is larger than EVERY number and not merely EVERY OTHER number which means it’s also larger than itself.
Infinitesimal refers to a number greater than (0) but smaller than every number of the form (\frac{1}{n}) where (n) is a natural number. An infinitesimal is thus a reciprocal of infinity. And since there is more than one infinity, there is more than one infinitesimal. (Thus, the reciprocal of the largest number is the smallest number greater than zero – the smallest infinitesimal.)