/sci/ - Science & Math

>not not A does not imply A
Was he right?

>>15697095
and what do you think about intuitionism
from wikipedia :
>In the philosophy of mathematics, intuitionism, or neointuitionism is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality.

>>15496635
Brouwer. He looks like a ghoul.

Reminder that "discontinuous functions" don't exist.

look at dis nigga

>stuck on problem
>take nap
>wake up and know the solution to the problem

is there a better feeling?

>hero worship in mathematics

redpill me on this guy

>>10252059
speak for yourself

https://existentialtype.wordpress.com/2012/08/11/extensionality-intensionality-and-brouwers-dictum/

>The interesting conception of the propositions-as-types principle is what I call Brouwer’s Dictum, which states that all of mathematics, including the concept of a proof, is to be derived from the concept of a construction, a computation classified by a type. In intuitionistic mathematics proofs are themselves “first-class” mathematical objects that inhabit types that may as well be identified with the proposition that they prove. Proving a proposition is no different than constructing a program of a type. In this sense logic is a branch of mathematics, the branch concerned with those constructions that are proofs. And mathematics is itself a branch of computer science, since according to Brouwer’s Dictum all of mathematics is to be based on the concept of computation.

https://existentialtype.wordpress.com/2012/08/11/extensionality-intensionality-and-brouwers-dictum/

>The interesting conception of the propositions-as-types principle is what I call Brouwer’s Dictum, which states that all of mathematics, including the concept of a proof, is to be derived from the concept of a construction, a computation classified by a type. In intuitionistic mathematics proofs are themselves “first-class” mathematical objects that inhabit types that may as well be identified with the proposition that they prove. Proving a proposition is no different than constructing a program of a type. In this sense logic is a branch of mathematics, the branch concerned with those constructions that are proofs. And mathematics is itself a branch of computer science, since according to Brouwer’s Dictum all of mathematics is to be based on the concept of computation.

>>9801307
>Why do some people on this board say computer science a superset of math?
A supercategory, not a superset.

https://existentialtype.wordpress.com/2012/08/11/extensionality-intensionality-and-brouwers-dictum/

>The interesting conception of the propositions-as-types principle is what I call Brouwer’s Dictum, which states that all of mathematics, including the concept of a proof, is to be derived from the concept of a construction, a computation classified by a type. In intuitionistic mathematics proofs are themselves “first-class” mathematical objects that inhabit types that may as well be identified with the proposition that they prove. Proving a proposition is no different than constructing a program of a type. In this sense logic is a branch of mathematics, the branch concerned with those constructions that are proofs. And mathematics is itself a branch of computer science, since according to Brouwer’s Dictum all of mathematics is to be based on the concept of computation.

*blocks your unrestricted use of excluded middle*

https://existentialtype.wordpress.com/2012/08/11/extensionality-intensionality-and-brouwers-dictum/

>The interesting conception of the propositions-as-types principle is what I call Brouwer’s Dictum, which states that all of mathematics, including the concept of a proof, is to be derived from the concept of a construction, a computation classified by a type. In intuitionistic mathematics proofs are themselves “first-class” mathematical objects that inhabit types that may as well be identified with the proposition that they prove. Proving a proposition is no different than constructing a program of a type. In this sense logic is a branch of mathematics, the branch concerned with those constructions that are proofs. And mathematics is itself a branch of computer science, since according to Brouwer’s Dictum all of mathematics is to be based on the concept of computation.

>>9164811
stop using the LEM

Before the class begins, you must get on your knees and worship Brouwer and accept that he was the most highly-evolved mathematician the world has ever known, even greater than Hilbert!

are you a Intuitionist

https://en.wikipedia.org/wiki/Intuitionism

>hurr... if you have a map then your location is on the map!!!
Ok... THAT's your "theorem"???

What does /sci/ think of Intuitionist mathematics? I mainly work in functional analysis, so proof by contradiction is pretty essential. I want to convince myself rejecting the principle of excluded middle is stupid.

What are your meme-free thoughts on constructive mathematics, intuitionistic logic, type theories, etc.

Hi /sci/ What is your opinion on Constructive Mathematics? Is someone of you maybe involved in research in that area?

>>6551225
>Formalism