0
Gödel's incompleteness theorem was a theorem that Kurt Gödel proved about Principia Mathematica, a system for expressing and proving statements of number theory with formal logic. Gödel proved that Principia Mathematica, and any other possible system of that kind, must be either incomplete or inconsistent: that is, either there exist true statements of number theory that cannot be proved using the system, or it is possible to prove contradictory statements in the system.
Still curious? Ask our experts.
Chat with our AI personalities
Devin
Maxine
FranAdd your answer:
Earn +20 pts
Does Godels Incompleteness Theorem imply axioms do not exist?
No, not at all. The Incompleteness Theorem is more like, that there will always be things that can't be proven. Further, it is impossible to find a complete and consistent set of axioms, meaning you can find an incomplete set of axioms, or an inconsistent set of axioms, but not both a complete and consistent set.
What did godel did for mathematics?
He found the incompleteness theorem
Who came up with the incompleteness theorem?
Kurt Gödel, philosopher. mathematician, logician and famous paranoid at Princeton.
Why did the whole number system fail?
I am not sure what you mean by the number system failing. One possible failure is Godel's incompleteness theorems. According to the first of these, in any consistent system of axioms whose theorems can be listed by an effective procedure is not capable of proving all truths about the arithmetic of the natural numbers. In any such system there will always be statements about the natural numbers that are true, but that are cannot be proved within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
What is the probability that someone will answer at least one of the eight questions correctly?
The answer to this question depends on how easy or difficult the eight questions are. If, for example, the questions were based on Godel's incompleteness theorem it is very likely that nobody could answer them - ever.
