who is who in math?

[AntonioLao]

Who are the intuitionists? The logicists and the formalists? Are there anyone here belonging to any of this groups? Once you identify as a member of one the groups, this post is requesting enlightenment from whoever you are concerning your philosophical stand why math is useful to the progress of science and the humanities.

[Guille]

What is mathematical formalism?


I consider mself a logicist, but not to an exagerated extend. logicists believe that mathematics can not only be reduced and explaine din terms of a logical language, but that it is in full concordance with logic itself. I don't. I believe that maths can be reduced and explained by logic, but not that both re in full concordance. Please see my thread "Mathematics and Logic"

[AntonioLao]

I consider mself a logicist

So, you agree with what Frege did although his idea of building math on logic did have many appearances of paradoxes. Later, Russell and Whitehead continued to build the logistic school. However, this is my question: How do we use logic to answer Riemann Hypothesis in seeking where every prime to infinity will occur?

[Guille]

But I have a disticntion from Frege and the young Russell (when he discoevered his paradox, his change his view on logic), and it is that I believe tha math can be reduced to logic, but not explained by it.


About the infinite prime, well, I can asure you that it will be solve. It's a just a hypothesis that hasn't been proven. Is it in any way special? I doubt it. Fermat's last theorem made generations of mathematicians go crazy and/or depressed... But it was solved, around the time that I was learning to add and substract.

[AntonioLao]

The biggest prime question: Is infinity a prime number?

[Guille]

The biggest prime question: Is infinity a prime number?

WOW! These kind of questions are the kind of math questions that I love.

I think we shoudl first determine two things:

1. Is it a prime question or an infinity question?

2. Is infinity a prime or the prime sequence infinite?

[AntonioLao]

how about infinity plus 1? Is infinity plus 1 a prime number?

[Guille]

how about infinity plus 1? Is infinity plus 1 a prime number?

If and only if the space between prime numbers get's bigger each time you go upper in numbers, then infinity plus 1 cannot be a prime if infinity is a prime, or vice versa. Thus, either infinity is a prime, or infinity plus one is a prime, or none is a prime.

But this is if we treat infinity as a number, and if we believe that there is a difference between infinity and infinity plus 1. And I disagree with both of these.

[AntonioLao]

in binary notation infinity is ...111111111111111111111111111, there are infinite ones to the left. Adding another 1 wont change or break the sequence. Since a prime is defined as a number divisible by itself and 1 then infinity and infinity plus 1 are both primes.

[Guille]

in binary notation infinity is ...111111111111111111111111111, there are infinite ones to the left. Adding another 1 wont change or break the sequence. Since a prime is defined as a number divisible by itself and 1 then infinity and infinity plus 1 are both primes.

hummmm................

But that's the same as saying that 1.11111111111111111111111..... is a prime and so is tat number plus 1: 2.111111111111111111111....... Of course. But infinity doesn't have a size such as 1111111111111111111111111111...... or anything. It is a limit, and that's all. So itself cannot be sized and neither can any kind of infinity or addition ro multiplications includng infinite (s).