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You can see people go through that process right here on HN, slowly realizing that 1 the integer is the same as 1 the real number.
by auggierose 2y ago
You can see people go through that process right here on HN, slowly realizing that 1 the integer is the same as 1 the real number.
- empath75 2y agoThat thread felt like I was talking crazy pills. So many people confused by the difference between the construction of numbers using some particular set of foundational axioms and the properties of numbers that should hold true _regardless of the constructions_. Obviously the "integer 1" is not strictly speaking "the same as" the "rational number 1" when constructed in set theory, but there's a natural embedding of the integers into the rationals that preserves all the essential properties of the integer 1 when it's represented as the rational number 1. Confusing the concept with the encoding, basically.
- cjk2 2y agoI hope they aren’t all realising zero isn’t zero somewhere as well. I could really do without that headache today.