/sci/ - Science & Math

>>11710144
God can't exist without Peano postulates

>>11491130
In the First Order Logical Language of Arithmetic, there are four desirable properties we would like for our Theory of Arithmetic,

1) We would like it to be consistent.
2) We would like it be complete
3) We would like it to contain Peano Arithmetic
4) We would like it to recursively enumerable

What Godel's Incompleteness Theorem ultimately says is simply that there is no theory in this language that has all four of these properties. However, it is possible to show there are theories with any three.

Here's a good quote.

>>7684626
Well, no shit.

>>7684632
This guy gets it

Human knowledge is fundamentally incomplete, we probably can never prove anything with certainty. We use what works and is useful for us, but we might be wrong about everything. The thing is, you have to make assumptions because otherwise you'd never think about anything at all. We're constrained by how our minds work.

What makes something a complex number? Just an imaginary number with a real number component (e.g. 2i)?