For an introduction to real real analysis is an old book typically called the 'Baby Rudin' Principles of Mathematical Analysis by Walter Rudin.
It is tiny and expensive, as most college math text books are once you get past a certain level. No idea if there is something better now, it is from the 1950's and there are used copies in most used book shops for cheap (or there was). It has no definition of 'equals' but does have a concept of equivalent relations.
Dummit and Foote's Abstract Algebra book is a great reference, especially with the problem with AI pollution. Coming from a General Relativity background, it still took me two years to work through on my own.
I don't know any suggestions on a more modern approach of starting with type or category theory.
I am not really interested in constructivist math, it is a problem to get around for me, so maybe someone who is can chime in on a better path.
While not rigorous, this paper does a good job at explaining just how muddy the concept of 'equality' is.
For an introduction to real real analysis is an old book typically called the 'Baby Rudin' Principles of Mathematical Analysis by Walter Rudin.
It is tiny and expensive, as most college math text books are once you get past a certain level. No idea if there is something better now, it is from the 1950's and there are used copies in most used book shops for cheap (or there was). It has no definition of 'equals' but does have a concept of equivalent relations.
Dummit and Foote's Abstract Algebra book is a great reference, especially with the problem with AI pollution. Coming from a General Relativity background, it still took me two years to work through on my own.
I don't know any suggestions on a more modern approach of starting with type or category theory.
I am not really interested in constructivist math, it is a problem to get around for me, so maybe someone who is can chime in on a better path.
While not rigorous, this paper does a good job at explaining just how muddy the concept of 'equality' is.
https://arxiv.org/abs/2405.10387