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Building from axioms is entirely possible, and in fact you'll often see the construction of first the rational numbers from the natural numbers and then the rea
by r0uv3n 4y ago
Building from axioms is entirely possible, and in fact you'll often see the construction of first the rational numbers from the natural numbers and then the real numbers from Cauchy sequences or Dirichlet cuts within the first few weeks of studying mathematics in university.
The construction of the natural numbers itself is often not discussed deeply, but the actual details aren't all that hard.
- sobriquet9 4y agoEverything you know is easy for you. For others, there's opportunity cost. The time one spent on learning Peano axioms is the time one could have spent on learning something more useful, say, linear algebra.
- xigoi 4y agoYou can take all the well-known properties of numbers as axioms and study linear algebra. Then later, if you're curious, you can prove the presumptions from a smaller set of axioms.