202202
- I’m retrying because I gave up last time towards the end.
- Peano Axioms
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Sets deal with Infinity.
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They demonstrate their true power in infinite sets.
- It’s interesting how this connects to Haskell’s 61f0091b79e113000090095b.
- It would be very interesting to read this volume while learning Haskell.
- Russell’s Paradox
- Set operations and logical operations
- Sets defined by List Comprehension are closely related to logic.
- Well, that makes sense.
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Any abstract concept can be studied in mathematics if it can be expressed in sets or logic.
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Algebra, geometry, analysis, even mathematics itself#mathematics is doing mathematics.
- I don’t really understand, but maybe I’ll understand later (blu3mo).
- Sets defined by List Comprehension are closely related to logic.
- Syntactic Methods
- Epsilon-Delta Method
- Representing formal systems in arithmetic
- I understood the procedure, but I still don’t understand the intention or what I want to do.
- Consistency
- A system that can prove both a and not a is contradictory.
- I want to think about proving both the existence and non-existence of consistency in a system.
First reading in 202010
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To see through hidden Structure. There is an irreplaceable joy there.
- This really expresses the fascination of Mathematics.
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It’s okay not to understand immediately.
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It’s much better than thinking you understand. “This might be the meaning of what is written in this mathematics book. But in reality, I might not understand it yet.” It’s good to think like that.
- #dunning-kruger effect
- Definition
- While I find beauty in various aspects of mathematics, I don’t find the fundamental part of the mathematical system beautiful at all.
- I wonder why.
- Is it because it feels “real”?
- Or should I say, is it the intention of the “human” who tries to conform to reality?
- In other words, is it because I was shown that mathematics, as I know it, is nothing more than a formally constructed system that is convenient for humans?