4
votes
1answer
435 views

intensional equality in type theory

I want to know why we add an intensional equality in type theory to definitional equality ? What is the aim with this intensional equality ? thanks
6
votes
3answers
699 views

What is the status of irrational numbers within finitism/ultrafinitism?

According to constructivism a mathematical object to prove that it exists". There are several formulas to calculate pi, such as: so I take it ...
6
votes
0answers
934 views

Is there a finite-dimensional vector space whose dimension cannot be found? [closed]

Is there a finite-dimensional vector space whose dimension cannot be found? Assume, we have somehow constructed a vector space whose dimension is finite, but yet unknown. Is there always an algorithm ...
48
votes
8answers
5k views

Is there any formal foundation to ultrafinitism?

Ultrafinitism is (I believe) a philosophy of mathematics that is not only constructive, but does not admit the existence of arbitrarily large natural numbers. According to wikipedia, it has been ...