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/sci/ - Science & Math

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5181275 No.5181275 [Reply] [Original]

I read somewhere (it might have been on /sci/) that geometric proofs can prove things that aren't true.

Question 1: Are there any examples of this?

Question 2: Are there any theorems that have only been proven geometrically and in no other way? (Aside from, obviously, theorems about geometry.)

Thanks

>> No.5181288

>>5181275

that is a koala bear, from australia. pandas are black and white and are from china.

>> No.5181295

>>5181288
My mistake. Could you possibly extend your knowledge to my questions?

>> No.5181302

your question is so vague that its basically unanswerable

>> No.5181348
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5181348

>>5181288

>> No.5181356

>>5181302
This. OP, elaborate.

>> No.5181362

Perhaps you are thinking of proofs like this?
http://www.mathpages.com/home/kmath392/kmath392.htm

>> No.5181395

>>5181362
That's pretty much what I'm looking for, I think, thank you.

>>5181295
>>5181356
Non-geometric theorems can be proven using geometry. I read that these proofs can actually be unreliable (or perhaps just not rigourous). Are there examples of this? And for the second question, I can't see the confusion there.

>> No.5181497

You cannot prove something false unless you're in a logically inconsistent system. If you're in a consistent system, then all theorems in that system are 'true' as far as that system goes. Note that the theorems from different geometries (euclidean and non-euclidean) contradict themselves taken point-blank, yet both are 'true' because they have their own system.

If it is in this sense that you ask that euclid's elements can prove false things, then I would guess that it's not so. As long as you have an accurate understanding of the common notions and axioms, the system is logically consistent as far as I can see. However, once the foundations were being evaluated during the beginning of the 20th century, geometry was further formalized so as to be computable, since Euclid's geometry is actually incomputable in first order logic. I've heard that Tarski's geometry can actually be proven to be logically consistent.

But perhaps what you are actually thinking about is whether mathematical truth can be applied to reality and still preserve 'truth'. As far as logic is concerned, if your mathematical model fits reality, then truth will be preserved. Whether your model fits is entirely beyond math, and squarely in the realms of empiricism.

Cheers.

>> No.5181501

>>5181395
what do you mean by geometry? what do you mean by "proven using geometry"? what do you mean buy "things that aren't true"? what do you mean by "unreliable proofs"? what do you mean by "non-geometric theorem"?

>> No.5181523

>>5181497
That was useful.

Sorry for being so vague, /sci/.

>> No.5181561

You can use topos theory which gives you the Isbell duality, and hence an equivalence among many algebraic/geometric structures.