Do axioms in maths also have proofs?
Arceus02:
axioms are unprovable
ok..and the proof that I am demanding is also of axiom
so it means it can't be prove
Axioms are the statements which are considered to be true. They are the building blocks of maths. They are the statements which are considered to be true and we solve other questions based on considering that the axiom is true. And for the question you said about whether axiom can be proved or not: No axioms cannot be proved. This is because for proofing axioms, you need something. You need some building blocks to proof a axiom and in this case, the axioms itself are the building blocks.
If you consider to proof axioms, without using axioms, you will have nothing.And you cannot proof something using nothing. Without axioms, you cannot go ahead to solve other problems.
You can check this: Kurt Gödel's incompleteness theorem - It says that not every true statement can be proved. There's a video about this in Numberphile.
oh..okk dear...thank u so much for information
welcome :)
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A mathematical statement that we know is true and which has a proof is a theorem. ... So if a statement is always true and doesn't need proof, it is an axiom. If it needs a proof, it is a conjecture. A statement that has been proven by logical arguments based on axioms, is a theorem.
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