/sci/ - Science & Math

[Anonymous No.14506802]

Infinite sets exist even though we’ve never seen them. Undefinable real numbers are real even though it is never been proven that they are required to satisfy the real axioms. Some infinities are bigger than other infinities. Paradoxes are just a natural part of mathematics. There is no correct approach to mathematics, no system is true and consistent, you can just make up axioms as long as they appear to be consistent with each other, never mind the real world and intuition.

[Anonymous No.14506805]

>>14506802
ive never seen a natural number before. i’ve also never seen a bit.

[Anonymous No.14506814]

>>14506802
>never mind the real world and intuitio
This is mathematics, not your gay liberal arts crap.

[Anonymous No.14507113]

>>14506802
Well what you're treading on is called philosophy of mathematics. Paul halmos in his introduction to naive set theory says right out that you tend to presume that sets exist you don't prove that they do. And if you want to go one step further back you would have Parmenides well maybe that's more than one step, who says that all is one. So as soon as you're dividing one I've been to many the question then becomes where are the boundaries. And you can sort of have an IU view that says well there's a natural boundary say you have one piece of land and then a river and then another piece of land and then you can say that river is a natural boundary. The problem is there's land continuous the river is just water on top of that one piece of land. One way to think about this is to use a philosophical approach called pragmatism although I don't believe there's very much philosophy of math dealing with this directly although I think the philosopher Charles Sanders Pierce who is recognized as an American pragmatist was very much into mathematics. So when people do math they're trying to solve a problem like a literal problem for example they have sheep and they have no way to count them because they haven't invented counting yet but they can take a bag of stones and every morning they see the Sheep leave the Sheepfold and they put a stone into a pile. They do that for every sheep. Then every day when the Sheep come back they put a stone back into the bag. And then they know they have all the Sheep when there's no more Stones left in the pile. And they can do that without any notion of counting all they know is that if there's rocks in the pile there are still sheep out there.

[Anonymous No.14507118]

>>14506802
So it's even sort of questionable whether you can ever have a number without a unit. Like you can have one stone or 5 or 10 stones in this pile of stones representing the Sheep out of the Sheepfold but can you ever have a 5? What does that even mean?

[Anonymous No.14507153]

>>14507113
>>14507118
Yes I see what you’re getting at. Numbers are adjectives and arithmetic is simulation. To add 3 + 7 is fundamentally the same as writing 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1, which is defined as 10. So we just develop mental rules and memorize results of these simulations. All math is world modeling. For this reason it makes no sense to invest in set theory and other inventions

[Anonymous No.14507171]

>>14507153
Math comes from the Greek

EtymologyEdit

From the root ofμᾰνθᾰ́νω(manthánō,“I learn”)+-σις(-sis,verbal noun suffix).

So in this sense you could literally say that math is a sort of learned behaviour. And then the question becomes our people learning things that actually exist is math natural Are there natural numbers or are all numbers artifice that is Art. I would leave more towards saying numbers are invented to solve problems rather than that they naturally exist. However this gets that is Art. I would leave more towards saying numbers are invented to solve problems rather than that they naturally exist. However this gets a certain sort of mathematician very butthurt because he likes to think that his math skills are like a natural ability just like a football player is naturally good at throwing the ball and so forth. But math isn't actually like that math is just memorizing a bunch of arbitrary stipulations. That doesn't mean engineering or physics are like math it just means that the math component to those things is made out. You couldn't figure out that if you are carrying weight you move more slowly without any mathematical equations determining how much more slowly it would make you move given the same Force.

[Anonymous No.14507188]

>>14507171
>Math comes from the Greek