81 Math Symbols Explained 

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

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

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

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

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.

9² maths symbols explained

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

aleph sighted watch out for abnormalities

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

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!

Instructions unclear, my brain is now in meth

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.

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...

#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 subgroups/subspaces/subalgebras #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 ?

This brings joy to my heart. Thanks for making this video :D

Thank you so much!!! your content is so heplful

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.

#34 is also used for direct sum of modules in linear algebra

Very interesting seeing the logic philosophy symbols, learned that last semester and didn’t know if they actually counted as a math symbols lol. Haven’t seen it anywhere else.

So crisp and clean

Empty sets in Desmos have the value of 1 [ WHAT?! ]

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

✓Greatest integer function G.I.F. [•] f(x)

Amazing. Now we need this kind of videos for other languages like programming languages etc.

I’m a little surprised you didn’t include the top arrow for vectors and the hat symbol for unit vectors. As a side note, physicists tend to use * for the complex conjugate and † for the Hermitian adjoint.

sin(θ) ≡ ℑ(e^iθ) cos(θ) ≡ ℜ(e^𝔦θ)

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

"+" may also be used to denote that the operation requires the use of a Phillips head screwdriver.

imaginary? are you kidding me? They couldn’t cope with their math being wrong so they just made imaginary numbers

∑ is the sigma sigh💀💀

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

Not adding π, iota, theta is an unforgivable crime.

Thank you so much, I have always wanted to know these symbols.

xor symbol is also used to signify a direct sum in abstract algebra

I believe everyone regardless of their educational level will be pleased to watch this video. Very interesting content, may you can add more symbols that we often use. Such as degree (in angle and in temperature), arc... etc

Now I know how to hold a brush Tho you're art is a guid without rush I am satisfied with your flow The way it is, is with no flaw Very vry nice vid BTW I am not sure how you video in the time being has 500 likes It's Strang but keep the nice work

5:31 the integral isn’t necessarily an antiderivative but the difference between 2 anti derivatives can be a shortcut to finding the integral the integral is the sum of all outcomes of a function between a upper and lower limit (think of sigma but not limited to integers)

Knew most of them, but some were pretty cool and I will start using them when writing my maths note since it's easier than writing by hand haha

i thought this video wouldn't be long enough but your explanations are great good video!

In the starting, It was a maths video but in the end it a great grand IIT professor explaining computer language....

small correction for #80: the ray starts at the first point and PASSES THROUGH the second point, rather than ending at it.

In Desmos The tilde is used for regression

Our teacher taught us that the '±' can also be used to say 'or more' as in: It was around 50± = it was around fifty or more

What is special about the mathematical term in banner??

OG's will remember back when sigma was an actual math symbol

6:59 also omega represents 2nd.

The "~" sign also represents negation of a statement.

math class be like: **Problem:** Solve for \( x \) in the equation: \[ \int_{0}^{\pi/2} \left( e^{i\theta} + e^{-i\theta} ight) d\theta + \sum_{n=0}^{\infty} \left( \frac{1}{2^n} + \frac{1}{3^n} ight) + \lim_{x \to \infty} \left( \frac{1}{x} + \frac{1}{x^2} ight) + \left( \frac{\sin^2(x) + \cos^2(x)}{\sin(x) \cos(x)} ight) = 2x \] **Solution:** 1. **Integrating the first term:** \[ \int_{0}^{\pi/2} \left( e^{i\theta} + e^{-i\theta} ight) d\theta \] Recall that \( e^{i\theta} = \cos(\theta) + i\sin(\theta) \) and \( e^{-i\theta} = \cos(\theta) - i\sin(\theta) \). So, \[ e^{i\theta} + e^{-i\theta} = 2\cos(\theta) \] Thus, the integral becomes: \[ \int_{0}^{\pi/2} 2\cos(\theta) d\theta = 2 \int_{0}^{\pi/2} \cos(\theta) d\theta = 2 \left[ \sin(\theta) ight]_{0}^{\pi/2} = 2 (1 - 0) = 2 \] 2. **Evaluating the infinite series:** \[ \sum_{n=0}^{\infty} \left( \frac{1}{2^n} + \frac{1}{3^n} ight) \] The series can be split into two geometric series: \[ \sum_{n=0}^{\infty} \frac{1}{2^n} + \sum_{n=0}^{\infty} \frac{1}{3^n} \] Using the formula for the sum of an infinite geometric series \( \sum_{n=0}^{\infty} ar^n = \frac{a}{1-r} \): For the first series: \[ \sum_{n=0}^{\infty} \frac{1}{2^n} = \frac{1}{1 - \frac{1}{2}} = 2 \] For the second series: \[ \sum_{n=0}^{\infty} \frac{1}{3^n} = \frac{1}{1 - \frac{1}{3}} = \frac{3}{2} \] So, the sum is: \[ 2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2} \] 3. **Evaluating the limit:** \[ \lim_{x \to \infty} \left( \frac{1}{x} + \frac{1}{x^2} ight) \] As \( x \) approaches infinity, both \( \frac{1}{x} \) and \( \frac{1}{x^2} \) approach 0. So, \[ \lim_{x \to \infty} \left( \frac{1}{x} + \frac{1}{x^2} ight) = 0 \] 4. **Simplifying the trigonometric expression:** \[ \frac{\sin^2(x) + \cos^2(x)}{\sin(x) \cos(x)} \] Using the Pythagorean identity \( \sin^2(x) + \cos^2(x) = 1 \): \[ \frac{1}{\sin(x) \cos(x)} = \frac{1}{\frac{1}{2} \sin(2x)} = \frac{2}{\sin(2x)} \] At \( x = \frac{\pi}{4} \), \( \sin(2x) = 1 \). So, \[ \frac{2}{\sin(2 \times \frac{\pi}{4})} = \frac{2}{1} = 2 \] Combining all parts, the equation becomes: \[ 2 + \frac{7}{2} + 0 + 2 = 2x \] \[ \frac{4}{2} + \frac{7}{2} + \frac{4}{2} = 2x \] \[ 2 + \frac{7}{2} + 2 = 2x \] \[ \frac{4}{2} + \frac{7}{2} + \frac{4}{2} = 2x \] \[ \frac{15}{2} = 2x \] \[ x = \frac{15}{4} \] So, the complex version of the simple equation \( 1 + 1 = 2 \) with a more intricate solution is given by: \[ x = \frac{15}{4} \] all done by: \̶̡̼̂[̵̹̹̂ ̷̩̝̽\̴̞̩̂̚m̷̲͒̏à̵̗t̴̲̰̅h̵̳̾c̴͇͗͊à̵̠̐l̵̡̈́{̸͍̘͂A̵̰̼̐}̴̬̽ ̸͕̓+̴͇̿ ̴̡̤́̆\̵́͜m̴̺̦̓̂á̶̜̪ț̵͓̈́̊ẖ̸̛̙̒f̵̼̃̇ŗ̴̈́̎a̵̦͛͊k̷̢̼͑͋{̶̗͔͒̾n̴̜͚̔}̷̢̫͊ ̷̡̮̆+̵͍͊̓ ̵̛͔́\̷͙͉̈́͗G̴̺̩̓a̶͈͛̀m̸͕͒͆m̷̪̀a̷̤̓͊ ̶̗̎+̸̰̓ ̴͎̊ē̷̫͝^̶̠͌̉\̵̞͈̍̿l̶̯͚̔a̷͖̾m̸̖̼̎ḃ̴̿ͅͅd̸͇͓͆̚a̸̹͛̒ ̸̝͎̀+̴͕̬͊̒ ̶̜̈́̑\̸̢̳̈Õ̷͖̃m̷̟͘e̴̹̎g̸͕͓͛a̷̳̾ ̸̟̽̅\̸̡̫͂]̵̬̠͒̅

00:47 My stupid ass thought the square root was a tick.

There are many kinds of multiplication symbols including the dot . And X for ordinary one defined on scalars or vectors. ٨ for exterior product on IR³ or on the exterior algebra , And X inside a circle for the tensor multiplication on a tensor algebra. Off course we don't count the inner product On Hilbert Spaces as it is a composed one.

Fractional partof floor/ceiling function would have been good toadd aswell, denoted with {x}

Welp guys, he said sigma. Are we awaiting brainrots to finnaly learn something?

6:29 When the Brainrot takes over Math

The equal sign was created very recently (relatively). Before the sign was created. PPL used to write. "is equal to"

That escalated quickly

6:30 Sigma🗿🍷

6:30 Gen alpha ruined this one

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

2:28 Actually a lot of authors use \subset without the line underneath and till not mean strict inclusion.

ermmm what the Σ?

you missed a lot of important uses of the symbol and only showed the most basic ones

You have made some banger videos that have taught me half the maths I know But I have to say that this is my favourite video Keep it up 🫡

Can you do a video like this for physics and math constants like plank contant, euler, i=imaginary, c= light speed and so on?

In math logic #35 and #36 can be say as top and bottom to indicate truth and falsity value symbols

Erm what the 6:30

Bro did not speak English

Awesome 👍

7:59 No, it represents a ray with an endpoint at the first point and passing through the second, going off toward infinity. A ray does not have two endpoints.

6:29 SIGMA SKIBIDI TOILET

Here before 1 hour tickets here! 👇 👆 *No.* 🗿🍷

Damn, you are soo good!

Mathematics fact : you can represent a complex number by x+iy where x is the real part and y is the imaginary part. A sq root of a negative number will be a complex number. Where i⁰ is 1 and i¹ is i and i² is -1 if you plot it on graph you will get a circle of radius pi.

I did not know that rounding was denoted by that ...😮

7:48 if two lines crossed out means non-parallelism, does a crossed-out upside-down T mean non-perpendicularity?

In my university, symmetrical difference is denoted with a mere "-", never seen the other symbols, same with an up tack for a contradiction

2:16 In Ukrainian language there is a letter 'є'(ye) which is also a word that means "is" , it is quite interesting how close it is to the mathematical meaning of that symbol.

Here where I'm studying (Nantes, western France), blackboard bold typeface U denotes the group of all complex numbers of module 1

Brain: *You have lost internet connection, please try again later*

Not sure how feel that I somehow knew almost all of these already apart from a couple

Thank ya, I think i gotta learn some...

in british mathematics, the backslash \ sign stated at 3:05 is not used, instead it is a straight vertical line; |

6:50 Why does the middle of the number below infinity move slower here?

Nice, thanks 👍

My head hurt. I should be in summer vacation... 💀

I hope there will be a follow video with more interesting and specific symbols. Math notation needs more appreciation

B: The lower the number, the bigger it gets. 1/0 [base integer / zero possibilities -> infinite possibilities] 1/0=inf

The colors are cool

Math is a language, and often the symbols are still up to interpretation. ✖️is used for multiplying numbers, cross-products on vectors, cartesian/ direct products on sets, and likely has some more applications (ie. Field Theory/ Ring Theory) Symbols are usually representative of Relations, whereas we often describe theoretical relations with dummy-symbols: “A relation R relates elements from the structure S, such that for all x,y of S: xRy” - and we would give properties to R, such as defining Reflexivity, Symmetry, and Transitivity,,, which are necessary properties for defining Equality and Ordering. Ordering is described in books using ambiguous symbols, but the convention is well documented- literally, a “partial order” is typically given a < symbol (sometimes it looks more squiggly),,, this is because < behaves pretty much the exact same way (not technically). Numerals themselves, I believe, are / are related to Quantifiers. Instead of “For All” or “There exist” etc 4 = “Four” - is a symbolic representation of a quantity. One of the topics I study tries to recognize that numerals represent quantities, which allows us to use numbers to define Abstract concepts- knowing that Scalars are Tensors that are built on those concepts (so, I try to unwrap the paradoxes) ~ is also used for logical negations (predicate logic), is probably more common. Predicates, in my opinion are just one type of logical statement, and the behavior comes from their ancestors… But, it is arguably a linguistics topic that intersects math (not my expertise) # is sometimes used instead of R for relations- I’ve also seen it used in Topology as an operation for “gluing manifolds”,,, but idk anything about that subject. FunFact: The Union and Intersect symbols are used for set operations - they are also used for Families, with a slightly different notation (I forget which definition for “Family”,,, as it can mean many things)

3+4=7 3-4=-1 3×4=3·4=12 3÷4=3/4=0.75 3±4=-1 / (or) 7 (Approximately equal to 5)) 3 minus-plus 4=-1 / (or) 7 (I don't have the symbol) (/ means square root) /4=2, (cube root) ³/4=approx 1.59 3+4=7, 3×4=12, 3^4=81 etc. 3+4≠5 3+4≈7.001 3~3.001, 4~4.001

You can use a * for multiplication i think

I need more symbols

What’s the best symbol to express “let a = b?” I usually use an equals sign with a triangle over it, but it seems most people just write out the “let” instead of using a different symbol

uptack in #36 looks very similar to perpendicularity and coprime in #78

My teacher 1 week before the test:

No mention of the Blendau Smeuk or the hytol Hakka.

I feel like a golden retriever

Now i can finally define limits using only math symbols.

Arithmetic operators: plus (+), minus (-), multiplication (x or dot), division (/) Plus or minus (±) Range (-) Root symbol (√) Equal (=) Not equal (≠) Approximately equal (≈) or tilde (~) Proportionality (∝) Triple bar or equivalent (=) Less than ( Less than or equal to (≤) Greater than or equal to (≥) Much less than > Empty set symbol (∅) Number sign (#) In (∈) Not in (∉) Set inclusion (⊂) Proper subset (⊊) Union (∪) Intersection (∩) Set difference () Symmetric difference (Δ or ⊖) Negation symbol (¬) AND (&) OR (∨) XOR (⊕) True (T) False (F) Universal quantifier (∀) Existential quantifier (∃) Uniqueness quantifier (∃!) Conditional operator (→) Logical equivalence (↔) Basic number systems: N (natural numbers), Z (integers), Q (rational numbers), R (real numbers), C (complex numbers), H (quaternions), O (octonians), U (universal set) Prime (') for derivatives and dot (.) for Newton's notation Integral (∫) Function composition Logarithm (log or ln) Limit (lim) Real part (Re) Imaginary part (Im) Complex conjugate (bar over a complex number) Summation (Σ) Product (∏) Infinity (∞) Aleph (ℵ) Factorial (!) Binomial coefficient (nCk) Absolute value (|) Floor function (⌊⌋) Ceiling function (⌈⌉) Nearest integer function (round) Visibility line (-) Non-divisibility (/) Parallelism (||) Non-parallelism (∦) Perpendicularity (⊥) Coprime (/) Line segment (overline) Line or ray (→) Infinite line (↔) I hope this helps!

1) 1+1=2 2) 1-1=0 3) 1×4=4 4) 1÷3=1 5) 3±4=-1 / (or 7) 6) 3+2≈4.99 7) sin² x+cos²≡1 (a+b)²≡a²+2ab+b² 8) 53

This video is super helpful. :D