Good points, a large chunk of math is different formalizations of the notion of size, for example (in order of increasing absurdity): https://en.wikipedia.org/

Good points, a large chunk of math is different formalizations of the notion of size, for example (in order of increasing absurdity): https://en.wikipedia.org/wiki/Cardinality https://en.wikipedia.org/wiki/Cardinality https://en.wikipedia.org/wiki/Measure_(mathematics) https://en.wikipedia.org/wiki/Measure_(mathematics) https://en.wikipedia.org/wiki/Ultrafilter_(set_theory) https://en.wikipedia.org/wiki/Ultrafilter_(set_theory) https://en.wikipedia.org/wiki/Euler_characteristic https://en.wikipedia.org/wiki/Euler_characteristic https://golem.ph.utexas.edu/category/2008/02/metric_spaces.html https://golem.ph.utexas.edu/category/2008/02/metric_spaces.h... https://golem.ph.utexas.edu/category/2006/10/euler_characteristic_of_a_cate.html https://golem.ph.utexas.edu/category/2006/10/euler_character... (and of course there are certainly many that I'm missing) For more fun, see these slides from John Baez: https://math.ucr.edu/home/baez/counting/counting.pdf https://math.ucr.edu/home/baez/counting/counting.pdf