Mathematics Thread

[Cheif Operations Director]

Just a thread to discuss math things, I guess I havn't seen one so here. 

Edited February 8, 2020 by Cheif Operations Director

[Wjolcz]

I love math. It's great.

[Nightside]

Does geometry count? I prefer  geometry, myself.

[Cheif Operations Director]

Ofc it counts, all math counts for any comment. 

[Bill Phil]

I often find myself doing something with math that seems really weird but then it... works.

[Cheif Operations Director]

such as? 

[K^2]

On 2/8/2020 at 7:54 AM, Nightside said:

Does geometry count? I prefer  geometry, myself.

Split the difference?

[Cheif Operations Director]

what is the world is that

[K^2]

12 hours ago, Cheif Operations Director said:

what is the world is that

From perspective of mathematics, it's just a branch of algebra with some interesting geometric interpretations. But from perspective of someone who has to do a lot of computation geometry (game engine stuff) there is a very specific flavor of Geometric Algebra called Projective Geometric Algebra (PGA) that's just magical. In PGA, there are two kinds of special products called Join and Meet. A join product of two points is a line passing through these two points. A join product of three points is a plane that passes through these three points. A meet product of two planes is the intersection line, and a meet product of three planes is a point. There are also some compound operations that let you very easily construct perpendicular and parallel lines/planes, perform rotations and so on. You can basically take all the geometry, linear algebra, trig, and all kinds of transforms, and roll them into a single algebra with very simple operations. And if you don't mind just a little bit of memory overhead, it can have quite decent performance as well.

[Codraroll]

I might as well chime in with this little bit of math trivia, which makes a ton of sense when you think about it, but which still is very under-communicated in math curricula out there:

X% of Y = Y% of X.

Handy if you need to find, for instance, 4% of 75. It's a bit tricky. 75% of 4, however, is fairly simple. And the answer is the same. "X% of Y" really only means "Multiply X by Y and divide by 100", and it doesn't matter which order you do things in.

[kerbiloid]

1 + 0 → 1
1 - 0 → 1

=>

+ ≡ -

Discuss?

[Lisias]

17 minutes ago, kerbiloid said:

1 + 0 → 1
1 - 0 → 1

=>

+ ≡ -

Discuss?

There're not such thing as subtractions, they had lied to you at school.

What's exists is adding negative numbers. Since 0 has no sigh, 0 exposed the lie!

So

1 - 1 = 0	// Lie
1 + -1 = 0 	// The only True

 

[kerbiloid]

Just now, Lisias said:

There're not such thing as subtractions, they had lied to you at school.

There are no brakes, only gas reverse.

[Lisias]

8 minutes ago, kerbiloid said:

There are no brakes, only gas reverse.

To tell the true, there are no gas reverse. Only Kinect energy being converted into heat. Additions, additions, additions everywhere!

My God... It's full of additions....

Edited February 11, 2020 by Lisias
Entertaining grammars made less entertaining

[Hannu2]

14 minutes ago, Lisias said:

There're not such thing as subtractions, they had lied to you at school.

What's exists is adding negative numbers. Since 0 has no sigh, 0 exposed the lie!

 

There is subtraction and it is defined exactly as you wrote. Subtracting is adding with additive inverse. Additive inverse is negation of the number.

Zero has a special property of being additive inverse of itself. That's why a-0 = a + (-0) = a+0. Zero is also additive identity which means a+0 = a.

[kerbiloid]

40 minutes ago, Hannu2 said:

Zero has a special property of being additive inverse of itself.

Say, "all integer numbers" (-inf;+inf) are a coordinate axis.

It has no intersections with another axis or another specially accented point.

So, all points belonging to this axis are presumed to be equal.

How do we know that exactly this point is the "zero" with special properties?

Why do we not treat any other point (i.e. number) as the special one?

Say, if take "5" as the center of symmetry, it should be additive inverse instead of "0"?

So, then five is new zero?

Say, ok, we can take only one such point at once. But then doesn't this mean that we call "0" any number we wish to be additive inverse?

Edited February 11, 2020 by kerbiloid

[Hannu2]

34 minutes ago, kerbiloid said:

Say, "all integer numbers" (-inf;+inf) are a coordinate axis.

It has no intersections with another axis or another specially accented point.

So, all points belonging to this axis are presumed to be equal.

How do we know that exactly this point is the "zero" with special properties?

Why do we not treat any other point (i.e. number) as the special one?

Say, if take "5" as the center of symmetry, it should be additive inverse instead of "0"?

So, then five is new zero?

Say, ok, we can take only one such point at once. But then doesn't this mean that we call "0" any number we wish to be additive inverse?

Postulates of arithmetic defines which special element of number set is additive identity. Of course it can be named with any word or symbol, but it is one unique element with special properties. Here you can find proof that if binary arithmetic operation obeys commutative law its identity element is unique. Multiplicative identity element is one and it is also unique.

I think if you define operators which are not commutative, it is possible get more identity elements but your set is not anymore field and you can not use proven properties of field to handle arithmetic. But in any case I have not studied that kind of math and can not say much about it.

You should also notice that + or - infinity are not elements of integer set. It seems to be quite common error. If you define such elements your set is not anymore field and will have odd arithmetic.

Edited February 11, 2020 by Hannu2

[farmerben]

I've got a question/request.  You've probably heard of Eric Weinstein who has popularized the Hopf Fibration and fiber bundles in higher dimensional geometry.  I've been through a few Wikipedia rabbit holes etc, but I don't grasp the notation well enough to generate good statements with it.  I had enough math in college to know about Riemmann geometry and graph theory, but barely know how to use them.  So I'd love to find a Youtube lecture series or something that goes through advanced geometry at the level of advanced undergrad/masters degree mathematician.  Or also to find pages that sort of fill in the gaps as Wikipedia contains simple and advanced while omitting all the mid-level things that put it in context.  

 

Got any good links?

[Lisias]

2 hours ago, Hannu2 said:

There is subtraction and it is defined exactly as you wrote. Subtracting is adding with additive inverse. Additive inverse is negation of the number.

(emphasis is mine).

So there's no real subtracting - it's only adding with additive inverse with a fancy name.

[Dirkidirk]

I hate math

 

no regrets

Edited February 11, 2020 by Dirkidirk
no regrets

[kerbiloid]

3 hours ago, Dirkidirk said:

I hate math

But this thread isn't named "mathematics love thread", so why not.

[Hannu2]

4 hours ago, Lisias said:

(emphasis is mine).

So there's no real subtracting - it's only adding with additive inverse with a fancy name.

 

From extreme point of view there is not more "real" things than axioms and even they are sentences generated by Stetson & Harrison method which have not yet proved to be contradictory with each other. In any case word "real" does not fit with mathematics, which is abstract logical system which have nothing to do with nature or "real world". It just happens to be suitable tool for understanding and predicting natural phenomena.

[Lisias]

30 minutes ago, Hannu2 said:

In any case word "real" does not fit with mathematics, which is abstract logical system which have nothing to do with nature or "real world".

Yep. It's the reason I used emoticons, the whole thing is intended to be a joke on the Functors Theory, Subtraction would be "only" an Addition's endofunctor to itself.

Subtraction is a stunt needed only for Natural Numbers (with reserves - there're no possible solution for "1 - 1" for Natural Numbers, as it doesn't have the Zero). Once we stablished the concept of Integers, subtraction is essentially only a special case of Addition.

Subtraction isn't even a Property for the Natural Numbers, and (N,+) is a mononoid besides its identity element being a number that doesn't exists on the Natural Set - and this is a whole new subject for yet more infamous jokes!  

[pmborg]

Hey @Lisias

This is for you:

0,9999(9) is equal to 1 or... can never be considered 1 ? 

If you know the answer please state a mathematics prove, if you give up I will write the solution

[Lisias]

2 hours ago, pmborg said:

Hey @Lisias

This is for you:

0,9999(9) is equal to 1 or... can never be considered 1 ? 

If you know the answer please state a mathematics prove, if you give up I will write the solution

In which Set? In Natural and Integers Sets, there's no such thing as 0,99999(9)!!

However, on the Irrational Domain, given f(x) = x , Limit(f(x)) when x approaches 1 is considered 1.

Edited February 12, 2020 by Lisias
My mistake. 0.9999(9) is 9 * 0.1111(1), and 0.1111(1) is a rational number, as it's the result of 1/9.