81 Math Symbols Explained

The language of math.

[alex_kly]

Now I understand that the math language also has a lot of dialects..

[Cringeroni]

0:02 Plus
0:06 Minus
0:15 Multiply
0:20 Divide
0:25 Plus-Minus
0:32 Minus-Plus
0:47 Sqr. Root
0:55 Equals Sign
1:04 Not Equals Sign
1:09 Approx. Equals sign
1:17 Tilda
1:21 Proport.
1:25 Triple Bar
1:34 Less Than
1:40 Greater Than
1:46 Less/Equal
1:54 Greater/Equal
1:59 M. Less
2:01 M. Gre
2:05 Empty Set
2:08 Number
2:16 Membership
2:21 No membership
2:24 Inclusion
2:28 emph. Set inclusion
2:37 Proper subset
2:41 Union
2:49 Intersection
2:57 Difference
3:07 Symmetric Diff.
3:17 Negation
3:24 Or
3:27 And
3:31 Exc. Or
3:36 Tee
3:41 Up Tack
3:48 Un. Quant.
3:52 Ex. Quant.
4:00 Unique Quant.
4:08 Implied
4:16 Logical Equi.
4:22 Blackboard Bold Typeface
4:26 N
4:29 Z
4:31 Q
4:33 R
4:35 C
4:38 H
4:40 O
4:43 U
4:48 Lag. Not.
4:50 Der. Of f
5:00 Newt. Not.
5:01 Der. of var X
5:14 Lieb Not. Der of f with respect
5:23 Part. Der of f
5:28 Integral
5:43 Arrow
5:50 Func. Comp.
5:54 log
6:02 ln
6:09 lim
6:12 Fancy R
6:17 Fancy I
6:20 bar above complex
6:29 Sigma Func.
6:33 Capital Pi Func.
6:40 Infinity
6:45 Aleph
6:53 Fraktur C
6:59 Factorial
7:02 Bin. Coeff.
7:14 absolute value
7:21 floor
7:24 ceiling
7:30 near. int. func.
7:36 divisibility
7:41 no divisibility
7:41 parallel
7:46 not parallel
7:47 perp/coprime
7:56 line seg.
8:00 ray
8:05 inf. line

[daaa]

π, ∆, °, %, ∠, ∮, Nabla, and many more, but still most of the topics covered

[ombrezz]

3:18
Note for the logic symbols, it is also common to see negation as a line over a term, AND as multiplication, and OR as addition.

[InterstellarCreature]

Math is like meth, once you start using it properly you can't stop it

[tigerlover]

6:29
I can never see this the same after what my class has done to it.

Edit: Day by day I regret making this comment.

[raphdm]

The most underrated math channel ever, even if you've already started blowing up

[JRuiz]

The transitions between the text and the symbols are really mesmerizing, almost satisfying lol
I also learned about symbols that I have never ever used. Great video, keep it up!

[WindyHeavy]

The oplus sign (XOR) could also mean Direct Sums of groups, rings, etc. When an algebra or group is "graded", it can be decomposed into a direct sum of smaller algebras or groups.

[maddy_boy]

Math is like a video game, the more you level up, the more symbols or characters unlock.

[davidjones-zmbc]

you been really helpful till now,
have a nice day man <3

[LaTortuePGM]

#11 ~ can also mean (and is mainly used for) asymptoticity or arbitrary equivalence relations (as well as negation, but mostly by philosophers)
#14-#17 can also be used for
#34 the \oplus also means, and is mainly used for, direct sums between two spaces
#35 "R v ~R = T" you're setting yourself up for trouble with intuitionists lmao
#49 the universal set famously doesn't exist, in case you've never heard of russell's paradox
#57 "log without a subscript" is ambiguous, it depends on the surrounding discipline : in math it's usually base e (like ln), in physics it's usually base ten, and in cs it's usually base 2.
#60-#61 they're more usually written Re() and Im()
#62 can also be written with an * at the right side of the x, symbol which can also denote a dual space ; x̄ is also a common symbol for the average value
#70 "... from on the number line" as well as in the complex plane, although it's usually called the 'modulus' there
#81 damn, i've literally never seen that one ! i'd usually just write it (AB) at this point. do you have some sources that show this double combining double-ended arrow above thing being used ?

[kenzou]

WHERE WERE YOU WHEN I WAS DOING MY BACHELOR'S IN MATH YOU WOULD HAVE HELPED ME THROUGH SO MUCH CONFUSION

[ZiaRahmanlive]

As a person whos about to finish elementary school my brain is turning into popcorn.

[Lilly-Lilac]

Some other uses for specific symbols:
1:17 Can be used as a relation in set theory
3:14 Right symbol can be used for a discrete change
3:28 Exterior product/wedge product
3:32 Direct sum
4:28 Almost every blackboard bold letter is used somewhere. F and K are used for fields. Blame the Germans for that one.
4:52 I have seem ' used for practically anything. Inverse of an element, complement, you name it.
5:27 Curly d is used for the boundary of something. For example, it's one of a few ways of notating the boundary in topology.
5:53 There are many different kinds of integral and variations on the symbol. For example the path integral, notated with the usual symbol with a circle on top is the integral along a closed curve.
5:43 It is more commonly used to show what an element maps to as part of a function.
6:18 Please never use mathfrak if possible. This is a personal request.
6:21 Sometimes used to represent cosets. Maybe this was just my prof? Who knows.
7:17 It can sometimes be used for any arbitrary metric, although this drives me insane.
8:00 Also can just represent any geometric vector.

[FireyDeath]

Kinda funny and a bit strange how he didn't explain parentheses, certain numbers and values like π, φ, θ, ε and ω, trigonometric functions, integral variations, lines and planes like ℒ and 𝒫, and more...

[eliximinatus]

aleph sighted watch out for abnormalities

[spike_curvball]

Instructions unclear, my brain is now in meth

[tttttttttttttttttt]

Thanks for the video, it helped me learn calculus, logic, sets and logarithm at 12

[phibik]

I learnt all of these the hard way, this is a good video for beginner in math notation