Re:Ask HN: Threshold Concepts in Mathematics
by Someone on Monday June 02, 2025 @05:23AM
(#44157058)
“Infinities are weird” might satisfy your criteria.
It surfaces in such things as
- why do we consider 0.9̅ and 1 to represent the same number?
- why are there ‘as many’ even integers as there are integers, and ‘as many’ integers as there are natural numbers?
- why are not all infinites equal?
If you don’t know/accept these, you’ll keep using intuition that served you well for many, many problems on finite sets on problems involving infinite sets, with disastrous results.
It surfaces in such things as
- why do we consider 0.9̅ and 1 to represent the same number?
- why are there ‘as many’ even integers as there are integers, and ‘as many’ integers as there are natural numbers?
- why are not all infinites equal?
If you don’t know/accept these, you’ll keep using intuition that served you well for many, many problems on finite sets on problems involving infinite sets, with disastrous results.