I'm convinced algebra is a scam

I'm convinced algebra is a scam.
Come laugh at me and prove me wrong.
I'm skipping imaginary numbers(i.e. shit people just made up), division and all the rest but the same argument applies to all of that I just don't have all day to write an essay.

Humans naturally understand stuff like if I have 9 apples and you give me another apple I have 10 apples. 1+1 = 2.
But then someone comes along and says instead of writing [math] 2+2+2+2+2=10 [/math] lets write [math] 2*5 = 10 [/math] and most get it, but some people don't and get confused.
But then someone says hey what if we replace numbers with letters, so you get
[math] 10 = x + y [/math].
And you fool some people, but most get wise to it and learn how variables work so someone else says what if we rewrite multiplications as [math] 10 = 5^2 [/math].
And again you fool some people, but most figure out that it's still the exact same thing written differently.
Then they start combining the stuff and end up with [math] f(5)=x^2 [/math] and you usually lose most people here, even though it's still just [math] 2+2+2+2+2=10 [/math] only rewritten in an extremely over complicated way. And don't even get me started on order of operations / p.e.m.d.a.s.shit.
But it just keeps going [math] f:5 &\X\longrightarrow x^2 [/math] and going and going and going.

What i'm saying is addition is the only real idea in algebra and everything else and I do mean everything else, from subtraction, to multiplication, to order of operations, to functions, is just another way of rewriting addition.
Tell me why i'm wrong.

You aren't wrong.

Even if everything could be expressed as additions, people wouldn't use it like that. From multiplying instead of adding the number n times to einstein's notation, everyone will use the simplest way to write an expression. We are lazy, and we create conventions to be able to write less while understanding what we do.

Does this argument hold true for calculus and the rest of math?
I was only ever taught algebra in school.

5^2 is not 10

Your right, its been a long time since I did algebra.
I did that old slip up.
Should be 25 = 5^2
and
5+5+5+5+5 = 25.

My logic still stands though.

15**2 = 10

wtf

"The only real number is 1. Everything else is just more of that." - David Mitchell

I have not used ^ in a long time, forgot how it worked.

It's a fairly obvious conclusion, like how 3+2 =5 but you would choose to write 5 as as a shorthand because it's autistic to say that you have (3+2) apples or something.

Algebra performs that function as a shorthand. Why would you wan to derive the formula every single time you do specific problem when you can just use an easier simplified version that applies to every single problem that involves that equation.

It essentially reduces time and resources, which I think you would agree is something very useful even if it sometimes get too abstract.

every bounded set of real numbers has a least upper bound

[math] 10=5^2 [/math]

Since fucking when is [math] 10=25 [/math] ?

>t. brainlet

I thought like you for some time, but I never got to say that Division and Subtraction were the extension of addition tho.

I wonder what does that mean for the rest of mathematic discipline. It's all just an extensions of adding?

...

What the fuck are you even talking about?

Addition is arithmetic, retard.

What about [math] \frac{1}{2} [/math] ?

I agree. It's just that math was never presented to me like this growing up. It was always presented as this mystical complex set of runes you had to memorize and doing so proved that you were smart.

>I wonder what does that mean for the rest of mathematic discipline. It's all just an extensions of adding?
That's really what im asking. I never had the opportunity to study past algebra.

Fine. But that's not what i'm arguing.

every convergent sequence is cauchy

>addition is the only real idea in algebra

Yes that is true. I don't know what your point is OP. The additional notation is meant to simplify complex levels of addition, but it isn't necessary.

>I don't know what your point is OP.
I was always bad at math and I just came up with this on my own so I was expecting to be wrong.

I was just throwing it out there to have it be disproved and maybe learn something from it.

I was not trying to make a point or even be right.

Everything is presented like this. It's not just math.

The first two years of biochemistry are literally just learning the language. Learning how to name things and identify molecules. It's so tedious and it's due to our human limitations. We can't perform telepathy so we need to transcribe everything, which is very inefficient. Real learning doesn't happen until many years of study, when you finally know enough to enter the ring.

Every time I think I've seen the most retarded shit possible on Veeky Forums, a thread like this comes and proves me wrong. Bravo, op.

ok but say why

I'm utterly convinced that this thread is just a very elaborate and well-done troll. No one can actually be this stupid.

ok but say why

This is why I made this thread. Tell me why im wrong.

Mathematics is a 2D language.

What the fuck is that? Once you start stacking numbers on top of each other logic goes out the window.

You have to be either a troll or still in middle school, I refuse to believe that anyone could possibly be this ignorant.

learning math becomes a lot easier once you realize that it is more about learning the language of math than than a perfectly continuous system of logic, which it is not

every tenure-track sequence is cushy

>[math]5^2=10[/math]
Nice troll, algebra is hard because you suck
But really algebra is a very large field that goes stretches from linear algebra with matricies to abstract algebra with rings and groups. It isn't the study of arithmetic like you make it out to be, that is just arithmetic. Algebra is the study of structure in mathematics in isolation to the thing the structure refers to. Like studying what multiplication like operation do to objects and how multiplication should extend to further groups of numbers like complex numbers and quaternions. Hamilton derived the quaternions by looking at how their respective additive identities should behave under a finite multiplication group and went from there.

I was kind of disappointed when I found out that complex numbers were just vectors and that's why they worked the way they did.

...

I don't think you're giving enough credit where credit is due. All these ideas you mention took a very long time to develop and even longer to have the simple and useful notation you see now. Look at how algebra was originally done and you'll see what I mean. Instead of taking an entire page of work we can write it down as a few simple equations, which are then also easily solvable using specific rules. Hell it was even done in the form of poetry in some places.

Arithmetic isn't the only base you can build off of like you are saying. The Greeks didn't do any arithmetic or algebra at all. They did geometry exclusively. If they had to do something involving numbers they would turn the problem into a geometric problem, then solve that. The square root of a number is not a number to them. Instead the number you start with is the length of the side of a shape, then the square root is another shape you can physically draw. This is a big reason why the irrationality of the root of 2 was so disturbing they killed the guy who proved it. Up until this moment math was something purely physical and real, relating the actual measured lengths of different things. Now it was no longer the case. The pythagorean theorem says a right triangle with two sides having length 1 must have the third as sqrt(2). But you can't have sqrt(2) since it's irrational, cannot be expressed as a proportion of lengths. Shocking right?

Modern math is extremely broad and powerful. You mentioned imaginary numbers so I'll give you an example of their use. Consider the integral of 1/(x^2+1) from -inf to inf. Geometrically, this is the area underneath the curve y=1/(x^2+1) and the x-axis. If you know some calculus then you know this is just arctan evaluated at the infinities which gives pi. Another way you can do it is using Cauchy's residue theorem. I'll show the process in the next post.

(cont)
1) Factor 1/(x^2+1) into 1/((x+i)(x-i)). This is true since (x+i)(x-i)=x^2+ix-ix-i^2=x^2-i^2=x^2-(-1)=x^2+1.

2) Extend the problem in the complex plane where the x-axis is the real part of a number and the y-axis the imaginary. i.e. The number 1 is at (1,0), i is at (0,1), 2+i is at (2,1) etc. Now the integral from -inf to inf is the integral on a contour along the x-axis.

3) The singularities of 1/(x^2+1) are at x=i and x=-i. Cauchy says we can freely stretch the contour and the integral remains unchanged as long as we don't pass any singularities. If we do pass one we have to add 2pi*i*[the coefficient of 1/(x-a) in the power series expansion(1+1/x+1/x^2+...) at the singularity, where a is any number], this is called the residue. The reason for this is because the integral of 1/z dz along a circle is 2pi, since dz/z = d(re^it)/(re^it)=(ire^it dt)/(re^it) = i dt and since t goes from 0 to 2pi in the circle the integral is 2pi*i.

4) Stretch the contour across the singularity at x=i, (0,1), into a big semicircle. Continue stretching it out away from the origin. Since 1/(x^2+1) goes to zero as the radius increases we can stretch the contour out to infinity and make the value of the integral along it zero. Now we just have to add the residue at x=i. Using the factorization in 1) we have 1/(x^2+1)=1/((x+i)(x-i)) so the coefficient of 1/(x-a) is 1/(x+i). Now around x=i, 1/(x+i) is around 1/(i+i)=1/(2i). Use Cauchy to get 2pi*i*[1/(2i)] = pi.

I realize you probably won't understand most of that. The point is that math is a very big thing that you currently know very little of. It isn't just addition and counting, nor is it just geometry. It's something more than that, beyond just the physical. Restricting your view to just real things is not just very limiting in what problems can be solved easily, but also flawed in like the sqrt(2) and triangles being incompatible concepts.

Mfw op is either absolutely dreadful and representative of 70% of this board or a troll and all the posters in here are high school brainletss who don't even know how to compute 5^2

Aside from OP's arithmetic mistakes he's realized something that 99.9% people overlook because of how simple it is, which is that everything in math is some type of addition with some conditions attached to it. If we look at how negative numbers are represented in most binary, non-quantum scale digital circuits, then this insight reaches an even greater depth and OP's stupidity for saying that [math]10 = 5^2[\math] is outweighed by the depth of his insight.

Bravo OP, bravo.

Also sage because of how retarded this fucking thread is.