Algebra Symbols: What Are They, and What Do They Mean?
Math can be difficult for those of us that prefer letters and words to numbers and symbols. However, it is important to recognize that even symbols, like those used in algebra, have names, and those names are made up of letters and words. But what are the names of these symbols, what do they mean, and how are they used?
For those of us that don’t really care for math, it might help to know more about the symbols used. Let’s explore the names of common algebra symbols used in both basic algebra and more advanced levels.
Basic Symbols Used in Algebra
If you have taken Algebra I, you will probably recognize a lot of these symbols. They are also used in advanced algebra classes. If you have not taken Algebra I yet, you can try this online course. It will give you a better idea of how to use each of these symbols. Some of these symbols are also repeated from basic arithmetic.
Symbol  Name and Meaning  Example Problem 

+  addition: to add something to another something  14 + 6 = 20 
–  subtraction: to subtract something from something else  13 – 10 = 3 
·  multiplication: to multiply something with something else, designed so x variables don’t get mistaken for multiplication  12 · 6 = 72 
/  division: to divide something by something else  150/5 = 30 
√  square root: to divide a number by its perfect square, also known as a radical  √4 = 2 
( )  parenthesis: grouping symbols, also known as round brackets  2 + (7 – 3) = 2 + 4 = 6 
[ ]  brackets: grouping symbols, also known as square brackets  2 + [7 – (3 + 6)] = 2 + (7 – 9) = 2 – 2 = 0 
{ }  set symbols: used for showing sets, also known as curly brackets when used as another set of brackets  set: whole numbers = {1, 2, 3, …}
curly brackets: 2 + {7 – [3 + (6 – 4)]} = 2 + [7 – (3 + 2)] = 2 + (7 – 5) = 2 + 2 = 4 
=  equals: to show what an equation’s answer is  3 + 7 = 10 
≈  about: is approximately equal to  Π ≈ 3.14 
≠  not equal: to show that it is not a correct answer  2 ≠ 3 
<  less than: one item has less value than another  2 < 3 
≤  less than or equal to: one item has less value than the other or equal value to the other  2 ≤ 3 
>  greater than: one item has greater value than the other  3 > 2 
≥  greater than or equal to: one item has greater value than the other or equal value to the other  3 ≥ 2 
⇒  implies: implies that if one thing is true then the other must be too, also known as if… then statements  7 and 5 are odd ⇒ 7 + 5 is even 
⇔  iff: if and only if, can also mean is equivalent to  7 = 4 + 3 ⇔ 4 = 7 – 3 
∴  therefore: some value is equal to another value meaning the opposite will also be equal  a = b ∴ b = a 
As you can see, there is a lot of them. The symbols implies and iff are used mostly in Algebra II, and you can take this online Algebra II course if you need more help on that subject.
Other Uncommon Algebra Symbols
There are more algebraic symbols, but these are usually used in more advanced algebra courses. Some of them use letters from the Greek alphabet like Sigma and Delta. Here is a list of these symbols and their meanings to help you with your advanced algebra courses.
Symbol  Name and Meaning  Example Problem  

x  variable: an unknown value that needs to be found, other letters from the alphabet can be used as well  2x = 4
2/2x = 4/2 x = 2 

∝  proportional: proportional to  ƒ(x) ∝ g(x)  
∞  lemniscate: infinity  ∞ + 1 = ∞  
⌈ ⌉  ceiling brackets: round the number up to the next whole integer  ⌈4.3⌉ = 5  
⌊ ⌋  floor brackets: round the number down to the next whole integer  ⌊4.3⌋ = 4  
!  factorial: multiply a number’s factors together to get a new number  4! = 1 · 2 · 3 · 4 = 24  
   absolute value: find the absolute value of the number inside   5  = 5  
ƒ(x)  function: maps values of x to  ƒ(x) = 3x + 5  
(ƒ ο g)  function composition: multiplying functions together  (ƒ ο g)(x) = ƒ(g(x))
ƒ(x) = 3x, g(x) = x – 1 → (ƒ ο g)(x) = 3(x1) 

Δ  delta: change or difference  Δt = t_{1} – t_{0}  
Σ  sigma: summation, a sum of all values in a range of series  Σx_{i} = x_{1} + x_{2} + … + x_{n}  
e  e constant: also known as Euler’s number, e = 2.718281828…  e = lim(1 + 1/x)^{x}, x → ∞  
γ  EulerMascheroni constant: a constant number, γ = 0.527721566… 


φ  golden ratio: a constant known as the golden ratio, φ = 1.618…  φ = a/b = (a + b)/a 
As you can see, some of these are far more complicated than most algebra symbols and involve more math than most high school students are required to take lately. The golden ratio is also a Greek letter like Sigma and Delta, and the EulerMascheroni constant is also a Greek letter.
Matrix Algebra Symbols
There are specific symbols that have a different meaning in regular algebra that are used in a new way when taking matrix algebra. If you have not taken matrix algebra yet, try this online course. Here is a list of the common symbols and their meanings used in matrix algebra.
Symbol  Name and Meaning  Example Problem 

[ ]  brackets: matrix of numbers  ⌈6 4 24⌉
⌊1 9 8⌋ 
A⊗B  tensor product: the most general bilineral operation, used for matrices and other algebraic equations  V⊗W := F(V ⋅ W)/R 
A^{T}  transpose: matrix transpose  (A^{T})_{ij} = (A)_{ji} 
A^{†}  Hermitian matrix: matrix conjugate transpose  (A^{†})_{ij} = (̅A)_{ji} 
A^{1}  inverse matrix: the reciprocal of a matrix  A A^{1} = I 
rank(A)  matrix rank: the rank of the matrix A  rank (A) = 3 
dim(U)  dimension: a dimension of the matrix A  rank (U) = 3 
Final Notes
There are many more symbols in math that are not necessarily for algebra, and even this list does not cover every single algebraic symbol. The best way to learn the math symbols needed for your class is to take that class. If you are interested in more practice for algebra, try Algebra 1 Made Easy, Algebra I: Straight to the Point, or Beginning Algebra: Building a Foundation. These courses are available online, and most of them are available on most mobile devices as well. If you have any other algebra symbols you’d like to share, just leave them down in the comments.
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