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You won't be able to complete a single formal, rigorous proof without clear, formal unambiguous rules. Yes, first principle reasoning is straining, requires har
by Kenji 11y ago
You won't be able to complete a single formal, rigorous proof without clear, formal unambiguous rules. Yes, first principle reasoning is straining, requires hard work and causes headaches, but the understanding will be deeper and complete. The English language is shaped by use and constantly changing. Mathematics is not supposed to change unless we have a mistake in our axioms.
- anigbrowl 11y agoConsider imaginary numbers, which don't invalidate anything as such and have to be tidied away after you're done playing with them, but make an entire class of calculations much easier by providing a consistent way to deal with otherwise awkward problems.
- Kenji 11y agoThey don't change the existing parts of the language, they just enlarge its body. Imaginary numbers don't invalidate the other rules. In natural languages, if you learn the rules down to the last nit-picky detail, you will soon realize that it is no longer valid, sometimes within years, other times within decades.