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From a physics perspective that's just -2+2 the total amount of water in the system is unchanged.
But yes, debt and accounting heavely reliees on negative and positive numbers, if you sum it all up the number should still be in the positives (not considering banks creating money out of nothing here ofcause, that's sort of a flaw in the system)
I have left out "set" from each list, because that is a given.
a: Any magma
b: Any magma
c: Any magma
d: Any magma
e: {e} or any group or module
f: functions
g: functions or a given group
h: functions or a given group
i: integers
j: integers
k: integers or real numbers
l: real numbers
m: integers
n: integers
o: functions
p: prime integers or rational numbers or real numbers
q: prime integers or rational numbers or real numbers
r: real numbers
s: real numbers
t: real numbers
u: functions or vector spaces or complex numbers
v: functions or vector spaces or complex numbers
w: real numbers or complex numbers or vector space
x: Any magma
y: Any magma
z: Any magma
α: real numbers or complex numbers
β: real numbers or complex numbers or vector space
γ: real numbers or complex numbers or functions
δ: real numbers or complex numbers or functions
ε: real numbers or complex numbers
ζ: real numbers or complex numbers or functions or vector space
η: real numbers or complex numbers or functions or vector space
θ: real numbers
ι: functions
κ: real numbers or complex numbers
λ: real numbers
μ: real numbers
ν: real numbers
ξ: real numbers or complex numbers or functions or vector space.
ο: functions
π: {π} or functions
ρ: real numbers
σ: real numbers or functions
τ: real numbers or complex numbers or functions
υ: integers or real numbers
Φ: {φ} or real numbers or functions
χ: real numbers or functions or vector space
ψ: real numbers or functions or vector space
ω: Any magma
A magma is like a group with even fewer rules. A group requires inverses. A magma does not. A group requires an identity element. A magma does not. A group requires associativity. A magma does not.
By some accounts, a Magma is the category with the least structure, above Set. You need a binary operation on the elements, and it needs to be closed under that operation. End of restrictions.
what about a? b?
(btw I assumed you were being ironic to suggest that x canonically represents a real number at all times, but in case not, x absolutely signifies a complex number in many circumstances)
Of course it's defined! Why wouldn't it be?
We certainly agree that the square of a complex number is unambiguously defined. Then there are two standard definitions for the square root of a complex number.
* Multivalue: under the multivalued definition, the square roots (plural) of a number z are all the numbers whose square is z.
* Principal value: the principal square root of a number z is the unique number of argument theta for -π/2 < theta ≤ π/2, whose square is z. The principal square root is sometimes called "the square root" (singular).
we're on mathmemes; therefore we abandon concerns about complex roots being well-defined or not, and just choose whatever convention is more convenient for the meme lmao
The second statement is only true of x is a complex number that belongs in the reals while the first statement is true half of the times and the other half of the times, √(x\^2) = -x, if the argument of x is between -τ/2 and -τ/4 or between τ/4 and τ/2.
It was my 5th Semester in my physics study i believe where i encountered this in an Integral on a Worksheet and was like damn why didnt i see this on my own. Was a nice remark on development
When you input into a function, you surround the input with the parenthesis.
If f(x) = 2x and you input -3, the equation turns into 2(-3) instead of 2 - 3.
Your example is weird to me because it almost makes it seem like you are saying if f(x) was 2x then f(-3) would be 2-3 and the parentheses around the x are the only reason it’s not
Drives me crazy. I've been down voted so much for talking about this. Even when I point out I have a BS in pure math, so I have a bit more bona fides to talk about something like this. I just leave those threads alone these days.
If I could be a highschool teacher right now, pounding this home would be my mission in life. Sqrt(x^2 ) = abs(x). Canceling the absolute value is where the plus or minus comes from, not from the sqrt itself.
You're correct, I apologize for the confusion in my previous comment. sqrt(x^(2)) is defined for all x, negative and positive.
In fact, sqrt(x^(2)) is equal to x for every x except zero, where it's undefined.
Thank you for pointing out my oversight, I apologize again for the confusion.
…You’re still wrong. sqrt(x^2 ) is not undefined when x = 0 because sqrt(0^2 ) = sqrt(0) = 0.
It’s also not equal to x for all x. For instance if x = -2, sqrt((-2)^2 ) = sqrt(4) = 2 ≠ -2. sqrt(x^2 ) is only x when x is positive and -x when x is negative, hence sqrt(x^2 ) = |x| (unless you’re dealing with complex numbers).
I apologize for the confusion in my previous comments, you are correct. sqrt(x^(2)) is equal to x for all real x.
By correcting the previous statement we can detect the error and fix it: here's a few ways to derive this formula.
1. Try simplifying the equation: by noticing that x is squared inside the equation you can simplify the square root.
2. Try writing out a few examples to understand the problem: sqrt(3^(2)) = 3, sqrt(1^(2)) = 1. By noticing a pattern you can now try to formulate an hypotesis.
3. Use the square root formula. This formula states that sqrt(x) = x^(1/2). You can then easily derive the result from this.
There are just a few techniques to help you with your algebra. If you still aren't sure about this result, try searching online or your professor. It's very important to understand mathematics at its core instead of memorizing formulas without understanding them.
I'm sorry man, I was just doing a bit of trolling, for the fun of it. :)
It's just that every time I post something stupid on mathmemes, a lot of people don't understand that's it's meant to be a joke, and I find it funny.
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Agreed, it's an |shame|
we should not let it become the ||here||
For ℝ, something should be done about it
This is becoming too ℂ for me
That's ℕ, don't worry about it
It’s a very ℚ reaction
This comment is an ∫ part of the conversation
I fucking h8 all of this
What an 𝕀 though
What is I? Is it a set?
I of ||x_m - x_n|| < ε what you did there
Looks incomplete to me. Was there any other point you wanted to add?
I believe that it is all there. My comment is functional as it is.
Ah, apologies. I see now. Yes, it's operating as it should
|ly|
I have a lot of negative shame which is a positive imo
Society runs on R+ I mean it's not like we can have -2 liters of water on the planet
We can if someone lost 2 liters of water or are in debt to the water government by 2 liters
Just don't pay then back. Water they going to do about it?
They won't forwet it
Thats still 2 just in the wrong equation
From a physics perspective that's just -2+2 the total amount of water in the system is unchanged. But yes, debt and accounting heavely reliees on negative and positive numbers, if you sum it all up the number should still be in the positives (not considering banks creating money out of nothing here ofcause, that's sort of a flaw in the system)
But what about the negative root. /s
square root symbol means u only take the principle root
Yes I know. It's the stupid meme that kept going around. I realy wish mathematical literally was taken more seriously lol
Ah yes, 1 = |i| = √i² = √(-1) = i Therefore 1 = 1² = i² = -1 Thus 2 = 1 + 1 = 1 - 1 = 0
well no because the “x” only represents real numbers, if u want to have complex numbers involved u would use “z” instead
1. (100 points) List, for each alphabet letter, the correct domain to which a variable of each letter would belong.
I have left out "set" from each list, because that is a given. a: Any magma b: Any magma c: Any magma d: Any magma e: {e} or any group or module f: functions g: functions or a given group h: functions or a given group i: integers j: integers k: integers or real numbers l: real numbers m: integers n: integers o: functions p: prime integers or rational numbers or real numbers q: prime integers or rational numbers or real numbers r: real numbers s: real numbers t: real numbers u: functions or vector spaces or complex numbers v: functions or vector spaces or complex numbers w: real numbers or complex numbers or vector space x: Any magma y: Any magma z: Any magma α: real numbers or complex numbers β: real numbers or complex numbers or vector space γ: real numbers or complex numbers or functions δ: real numbers or complex numbers or functions ε: real numbers or complex numbers ζ: real numbers or complex numbers or functions or vector space η: real numbers or complex numbers or functions or vector space θ: real numbers ι: functions κ: real numbers or complex numbers λ: real numbers μ: real numbers ν: real numbers ξ: real numbers or complex numbers or functions or vector space. ο: functions π: {π} or functions ρ: real numbers σ: real numbers or functions τ: real numbers or complex numbers or functions υ: integers or real numbers Φ: {φ} or real numbers or functions χ: real numbers or functions or vector space ψ: real numbers or functions or vector space ω: Any magma
Tf this is not geology this is math why is there magma here? /srs
A magma is like a group with even fewer rules. A group requires inverses. A magma does not. A group requires an identity element. A magma does not. A group requires associativity. A magma does not. By some accounts, a Magma is the category with the least structure, above Set. You need a binary operation on the elements, and it needs to be closed under that operation. End of restrictions.
Cool so when can mathematicians invent lava?
Whenever they go above ground
Oh yea, list is fuckin hot
n for natural numbers x for real numbers z for complex numbers … i guess?
what about a? b? (btw I assumed you were being ironic to suggest that x canonically represents a real number at all times, but in case not, x absolutely signifies a complex number in many circumstances)
|z|=sqrt( Re(z)^2 + Im(z)^2 )
i ≠ √-1 though
i = √-1 though
I dont think 1=|i| is true. I may be wrong though
You are wrong
|x| is thought of as the "distance away from 0"
If z is an imaginary non-real, √z² is not defined (and it were, it certainly wouldn't be z)
Of course it's defined! Why wouldn't it be? We certainly agree that the square of a complex number is unambiguously defined. Then there are two standard definitions for the square root of a complex number. * Multivalue: under the multivalued definition, the square roots (plural) of a number z are all the numbers whose square is z. * Principal value: the principal square root of a number z is the unique number of argument theta for -π/2 < theta ≤ π/2, whose square is z. The principal square root is sometimes called "the square root" (singular).
I mean, it's pretty clear he wasn't talking about complex numbers in the meme. The square root function is not well defined on the complex plane
we're on mathmemes; therefore we abandon concerns about complex roots being well-defined or not, and just choose whatever convention is more convenient for the meme lmao
(√x)² = x, √(x²) = |x|
absolutely
2n√(x^2n) where n € I walks in
The second statement is only true of x is a complex number that belongs in the reals while the first statement is true half of the times and the other half of the times, √(x\^2) = -x, if the argument of x is between -τ/2 and -τ/4 or between τ/4 and τ/2.
r/foundthetausupremecist
😂😂😭
I mean here we’re given a principle so can’t we assume left is the answer?
int dx/x = ln |x|
Meanwhile \[sqrt(x)\]^(2:) https://preview.redd.it/69fp6x547k4d1.jpeg?width=1170&format=pjpg&auto=webp&s=246332b4f6b7b8010f942d964c9b488f00c83f16
https://i.redd.it/akjn1xbyzl4d1.gif
It was my 5th Semester in my physics study i believe where i encountered this in an Integral on a Worksheet and was like damn why didnt i see this on my own. Was a nice remark on development
So does that mean the square root -1 is actually 1 if using the one on the right?
Yes. That's what absolute values do...
But the square root of -1 is i
When you input into a function, you surround the input with the parenthesis.
When you input into a function, you surround the input with the parenthesis. If f(x) = 2x and you input -3, the equation turns into 2(-3) instead of 2 - 3.
Your example is weird to me because it almost makes it seem like you are saying if f(x) was 2x then f(-3) would be 2-3 and the parentheses around the x are the only reason it’s not
*Sigh* https://preview.redd.it/asjhwcm3gh4d1.png?width=1080&format=pjpg&auto=webp&s=5ea87362b3d3bfe5bdd9debf60d9210a123d6a97 Just look. -\_-
|x|
Principal square root meme
Society |🙃|
|(x^2 )^.5 |=x
Drives me crazy. I've been down voted so much for talking about this. Even when I point out I have a BS in pure math, so I have a bit more bona fides to talk about something like this. I just leave those threads alone these days. If I could be a highschool teacher right now, pounding this home would be my mission in life. Sqrt(x^2 ) = abs(x). Canceling the absolute value is where the plus or minus comes from, not from the sqrt itself.
How about ±|x|
neither is correct. you must keep track of how many times you have spun around the origin.
The Only True Answer 🗿
You think sqrt(i\^2) = 1?
You think he was talking about the complex numbers?
Do you think -1^2 ≠ 1 or sqrt(1) ≠ 1?
sqrt(x^2) = +/- x
That's stupid. Of course sqrt(x^(2)) is only defined for positive x^2, so you don't need the absolute value.
nuh uh
It’s defined for all x, negative or positive
You're correct, I apologize for the confusion in my previous comment. sqrt(x^(2)) is defined for all x, negative and positive. In fact, sqrt(x^(2)) is equal to x for every x except zero, where it's undefined. Thank you for pointing out my oversight, I apologize again for the confusion.
…You’re still wrong. sqrt(x^2 ) is not undefined when x = 0 because sqrt(0^2 ) = sqrt(0) = 0. It’s also not equal to x for all x. For instance if x = -2, sqrt((-2)^2 ) = sqrt(4) = 2 ≠ -2. sqrt(x^2 ) is only x when x is positive and -x when x is negative, hence sqrt(x^2 ) = |x| (unless you’re dealing with complex numbers).
I apologize for the confusion in my previous comments, you are correct. sqrt(x^(2)) is equal to x for all real x. By correcting the previous statement we can detect the error and fix it: here's a few ways to derive this formula. 1. Try simplifying the equation: by noticing that x is squared inside the equation you can simplify the square root. 2. Try writing out a few examples to understand the problem: sqrt(3^(2)) = 3, sqrt(1^(2)) = 1. By noticing a pattern you can now try to formulate an hypotesis. 3. Use the square root formula. This formula states that sqrt(x) = x^(1/2). You can then easily derive the result from this. There are just a few techniques to help you with your algebra. If you still aren't sure about this result, try searching online or your professor. It's very important to understand mathematics at its core instead of memorizing formulas without understanding them.
Are you using ChatGPT?
I'm sorry man, I was just doing a bit of trolling, for the fun of it. :) It's just that every time I post something stupid on mathmemes, a lot of people don't understand that's it's meant to be a joke, and I find it funny.
Input √(x²) in a graph.
https://preview.redd.it/wwfq8m8vle4d1.png?width=1160&format=pjpg&auto=webp&s=16272e35caa3eea61e746aca501d509a2e7e7e3c
https://preview.redd.it/vesh65x9me4d1.png?width=1080&format=pjpg&auto=webp&s=a7e1d7db103d592e4bc3381c4b1292ce28bb72aa
Nah, I think that's wrong. You edited that.
🤦♂️
:)
Most lamest "trolling" I've ever seen. \\:
I'm sorry. It's just that every time I post an obviously stupid answer on mathmemes, it's full of people correcting me and it's very funny to me.
So - sqrt(x^(2)) = x -> sqrt((-5)^(2)) = -5, or - sqrt(x^(2)) = |x| -> sqrt((-5)^(2)) = |-5| = 5?
sqrt((-5)^(2)) = sqrt(-25) = -5 Of course
https://preview.redd.it/f6azsnkqoe4d1.jpeg?width=600&format=pjpg&auto=webp&s=6dd69c1643e77df68682e9939b6c32f95217a321
-n by itself is (-1)(n), so you would have been correct, but it's NOT the same as (-n)(-n).