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>b-but Anon! Euclid is an informal system of mathe-
Let me stop you there. It can be proven formally, and verified using computerized systems
>b-but Anon, the fifth postulate.
Does have alternatives. Pic related. But Charles Dodgson went ahead and proved that Euclid's axiom results in the most simple determination of the 27th prop.
There is literally nothing wrong with Euclid. Prove me wrong.
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book related
http://www.unco.edu/nhs/mathsci/facstaff/Miller/personal/diagrams/euclid20thcenturyrivalsmiller.pdf
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It assumes the existence of reals, because for the objects to exist and have properties postulated by Euclid they have to have irrational coordinates, but as we all know perfectly well the reals don't exist, and therefore Euclid's axioms are logically incoherent and therefore are bullshit
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>>8598694
The existence of reals? The definitions are proofs enough. And they are hardly a priori. I don't believe you can really call anything a priori until you hit postulate five. Then you're dealing with two lines, two angles, and a postulate which depends on another postulate. I understand that mathematical judgments can be synthetical, however why is it that the definitions are necessarily informal?
The main problem lies in postulate five my friend and many agree that the definitions are solid and even can be formally accepted mathematically.
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>>8598694
All math has axioms.
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>>8598694
>It assumes the existence of reals
Stopped reading right there. You /wild/tards are truly the lowest life-forms
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