All Questions
4 questions
0
votes
0
answers
144
views
What are the First Principles of Euclidean Geometry (Besides the Axioms)?
On first principles, Wikipedia says:
A first principle is an axiom that cannot be deduced from any other within that system. The classic example is that of Euclid's Elements; its hundreds of ...
- 47
1
vote
0
answers
236
views
What is the current status of Foundation-of-Mathematics programmes?
I have been reading 'A Very Short Introduction to Mathematics' by Timothy Gowers and at one point he mentions that most of the mathematical proofs can be finally resolved to a set of logical ...
- 79
2
votes
4
answers
360
views
Is it possible to create an axiomatic system where 1+1 doesn't equal 2? What would be the consequences of such a system? [closed]
1+1=2 is a result (perhaps arguably more of a definition than a theorem?) of Peano Arithmetic, as well as other systems such as ZFC. I understand that 1+1 doesn't necessarily have to equal 2 if we ...
0
votes
0
answers
176
views
Is there an infinity of axioms in mathematics?
As I was trying to find a list of mathematical axioms used in modern branches of mathematics, I wondered if there's any meaning to the question of "how many mathematical axioms are there ?", and then ...
- 275