Math

No numbers are "real", they're all just tools we create to help us do math.

>what is a homomorphism

this map isn't even surjective

We must be defining multiplication differently. The set of imaginary numbers is not closed under the usual multiplication and thus not a ring under that multiplication.

It's over the imaginary numbers.

This, and if you define multiplication on the imaginary line as: a*b=a•b(-i)

I was going to call everyone ITT autistic then I realized I don't know what "real" number is supposed to mean either.

This whole stupid thread is constructed around the extremely ambiguous concept of "real". In the background lurks shitty old Plato. Get over your ancient misconceptions, you flatulent chan-tards.

was thinking that the bijection just needed to preserve distance for it to be a isomorphism.
This discussion has slightly helped my understanding.

That is an isometry, but to be fair sometimes isometries can be defined a distance preserving topological isomorphisms.

As a math teacher, I always convince my students this way

Can you show me negative apples?

Of course not, yet, we use negative numbers in grade school math, and life could not be possible without them.

Likewise, we cannot demonstrate i things, and yet we accept complex numbers as a fantastic way to solve certain operations.

By definition, no.

But then again the reals don't exist anyway, nor do large numbers. Circles that overlap do not necessarily intersect.

Am I being profound yet?

Why not just tell your students that complex numbers are a way of writing coordinates that have some unique advantages?

Why not just tell your students the complex numbers are the unique (up to fld. ext. iso.) algebraic closure of the real numbers?

Why not just tell your students to shut the fuck up and study for the test or they're going to be garbage collectors for the rest of their lives?

Why not just tell your students that math is a meme and supposed to be satire like most other memes?

why not tell your students what they actually are?
do you not know what they are, even as a school teacher? please tell me you aren't in my kids school district...

Yes because it works.

Math is not an invention.

I mean it was only 2 statements.

Sir Isaac netwad simply discovered calculus

what is it with amerilards and your shitty definitions of words

math is the objective truth derived from axioms. truth is real.

Did you mean Leibnitz, you filthy kike?

Jews made them up.

Suddenly all of it makes sense.

>math is not an invention.
Lol math is by its very definition an invention dude. its just stupid symbols to represent our world that we think are correct

jews are superior goy.

Prove truth is real then fuckwad. Then prove that that is real. Then take all your proofs and shove them up your ass.

Under addition they and the reals are isomorphic.

complex numbers are a 2D real manifold

trips of truth

if truth isn't real then what is real

q.e.d.

this

>tools we create
how can you create a tool which isn't real?

yes they're used in electrical fields. /thread.

You create it conceptually.

...

...

>prove truth is real
truth is real by definition

It is real, it's just made up.

Numbers are not positive or negative, real or imaginary. Numbers are on a spectrum of positivity, negativity, realness, and imaginariness

This. Work in DSP can confirm. Also cool people denote as j.

you're a literal drooling retard

>[math]\mathbb{C}[/math] is algebraically closed
>[math]\mathbb{R}[/math] isn't
>b-but they're the same
>t-they're even i-i-isomorphic!
jesus fucking christ never post again

an element of [math]\mathbb{R}[/math]

>solve
>an operation
please don't teach them English

He said the imaginary numbers, not the complex numbers.

all imaginary things are de-facto complex
everything complex can not be real, since reality is apparent and therefore simple, and therefore must be imaginary

therefore, the imaginary and complex numbers are one and the same

quod erat demonstrandum

C = R + iR = reals + imaginaries

Nothing in Mathematics is real. Just like its philosophical basis, it's abstraction. Intangible. However within this abstraction, "Imaginary Numbers" aren't actual numbers, they are a different kind of abstraction to numbers. Just as 1/4 isn't actually 0.25, rather a representation of it, even though it equates to it. It's useful, so we use it. If it gets results that are applicable to the real world then who cares how strange or arbitrary the abstraction seems.

>j love math

I don't get it

No. They are imaginary. Only real numbers are real.

WHY STOP HERE,

YOUR THOUGHTS ARENT REAL

YOUR PERCETION OF REALITY ISNT REAL

LIFE ISNT REAL

...

One's thoughts and thus one's self are plainly real, but that is the limit in terms of certainty.

Literally the definition.

you clearly haven't taken analysis.

real isn't real

I have, not that it is relevant as it is an algebraic definition.

Nope.

By "real", do you mean if reality demonstrates patterns as predicted by the use of imaginary numbers? If so, yes. Vector rotations, AC currents, and fractals all exhibit the properties deduced by the use of complex numbers.

They call them imaginary numbers, but there's nothing imaginary about them. Calling them fake simply because they're counter-intuitive is almost as insulting as calling negative numbers fake because you can't ever find a tree with a negative number of apples growing on it. They're simply different tools used for different things. Negative numbers can be thought of as debts, and imaginary numbers can be thought of as rotations.

underrated

REDPILL

Intangible != not real

Socrates pls.

>spectrums are a tool of the jew
Of course.
At this point I wouldn't even be surprised if they've found a way to corrupt set theory.

Truth isn't real

>Planes are not real
Explain this

that's a fictional character, user.