How to pronounce “axioms” in English

axioms for God and for prayer and for the church and for Jesus all all for my

axioms in the book at all because they're super nerdy like they're just not you know I mean when you write a

- And axioms are, I guess, facts that we assume are true, based on which we then build the ideas of mathematics. So there's a bunch of facts, axioms about sets

And so the axioms on the list, these things like extensionality, express the most fundamental principles of the understanding of sets that he wanted to be talking about.

And you took the axioms, applied the logic, and you derived theorems.

A different set of axioms.

You wrote down some axioms, and then you proved some theorems.

And most of his axioms were pretty straightforward and undeniable.

of the axioms and premises or observation statements from which it proceeds."

people in axioms think about that, but I am

The first four postulates or axioms are like the minimum rules required to play that game, and then the fifth axiom selects the universe that you wanna play in.

So as long as the other axioms are consistent, adding choice won't lead to any contradictions.

- Can we maybe speak to the axioms that underlie ZFC?

And so are there a few basic axioms of it, or is it a meta pattern that describes things?

They'll frequently violate the axioms of rational choice.

And so you take these axioms, you derive out the way you expect a rational agent to behave, and this is what economic theory really is all about.

formal or you can have axioms in philosophy that are are much less

and so there was a worry about consistency of the axioms.

He wanted you to have a set of axioms, clearly defined system of logic.

There's the red and there's green and certain axioms about their own subjective experiences of colors.

uh Axiom axiomatic thinking self-justified statements now you can have axioms in logic that are very

sunrise and it's in that Spirit these axioms are meant to help people explore

and the continuum hypothesis and all these other sort of questioned axioms.

um so we call that dialectics right dialectics one of the axioms of this kind of geography of human geography

The axiom of choice can neither be proven nor disproven from the other axioms.

theory, there weren't any axioms there. He didn't have a list of axioms in the way that we have for set theory

It consists of the following main axioms: Axiom of Extensionality, Axiom of Empty Set, Axiom of Pairing, Axiom of Union, Axiom of Power Set, Axiom of Infinity, Axiom of

It was worked out in the way of Euclid's "Elements," with the axioms and proofs.

faith was sort of establish some some baselines for yourself you call those your axioms do you think you could give us a couple of those and help us

and I told him my story in solidarity and uh told him my axioms

But the notion of proof, of axioms, of deduction, this really was discovered by the ancient Greeks.

classical in nature the way self-reflective Consciousness has to work because it requires axioms that cannot be proven within the context of

Then in 1963, Paul Cohen proved there's also a world where all the axioms of set theory hold true except for the axiom of choice.

- I read some historical accounts by historians about that time period, specifically about Zermelo's axioms and his proof of the well-order theorem.

And so it's the statement that you start off with some rules, some axioms of your sort of mathematical framework.

They built a little software agent, which had certain axioms about colors and how they work.

It was sort of solved in a sense in that it's known that it doesn't follow from the other axioms of set

Same thing with mathematics, as long as you agree on the axioms up front of exactly what kind of a system you're playing with, then everything is well defined from there on out.

Then, you know unless of course there's issues with the axioms themselves with Godel and stuff.

Nowhere in the mathematical rule book was this explicitly permitted and math is built on rules, specifically axioms.

The Austrian mathematician, Kurt Godel, proved there is a world all the other already accepted axioms of set theory hold true, and so does the axiom of choice.

And so we have a lot of different axioms that describe the nature of this

So, I mean, the history of the current set theory axioms, known as the Zermelo-Fraenkel axioms, came out in the

- So ZFC sounds like a super technical thing, but it is the set of axioms that's the foundation of modern mathematics.

So, Zermelo introduced most of these axioms, I mean, as part of what's now called Zermelo set

- And we should say, in set theory, consistency means that it is impossible to derive a contradiction from the axioms of the theory.

And Euclidean geometry, you may have heard, is based on postulates or axioms.

Standard economic theory generation starts from a series of axioms-- primitive assumptions are taken to be self-evident.

Or else controversy, on the other side, it dealt only with pure theory; abstract reasoning from secure axioms, you know.