>people do number theory and arithmetic for thousands of years >only in 19th century someone comes up with axioms >no one cares about them except logicians these have no relevance to actual mathematics
>>8207503 The issue I have with them was introduced in the late 1800's/early 1900's. When logic was being formalized. Personally I'm surprised it wasn't caught considering many related results at the time.
>>8207518 Foundations are related to proof and theorem. You are correct that mathematics has been around longer than we've had axiomatization but that doesn't mean that modern mathematics is practiced without proof or theorem.
>>8207734 i think im using induction (i have a nonsci undergrad and im just seriously getting into mathematics). I believe the only assumtion ive made is that natural numbers are countable/orderable entities, and now ive gotten to a rational number field.
>uncountable sets im a few vids away from wildbergers assertion that the infinity set doesnt exist, which im anticipating with much excitation. Its math foundations ~16 or so on his youtube channel, njwildberger, if youd like to see what im seeing/following along with. He prefaced the series with the idea that he has a better approach, vids are now near #200 many of them 30+ minutes. I hope to catch up by 2017
>>8209013 I was using \ for 'less'. That first pic is for integers where an integer is two natural numbers a\b. Its wildberger's approach to negative numbers.
He defines rationals as a set of integers a/b. Zero as a rational number ends up being (1\1)/z where z is a non zero integer.
>>8208779 While many aspects are self evident, there are some very interesting things i have gleaned from this exercise. The most interesting has been the pattern/relationship between the basic operations
>>8209117 Whats the total area inside all of those ford circles then? You can probably give the answer, but most definitely not verify it since u seem to be wasting your times verifying the axioms of arithmetic. Be a real nigga and fuck with modular forms n shit instead of doing this pointless shit
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