Algebra Symbols: What Are They, and What Do They Mean?

algebra symbolsMath 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.

SymbolName and MeaningExample Problem
+addition: to add something to another something14 + 6 = 20
subtraction: to subtract something from something else13 – 10 = 3
·multiplication: to multiply something with something else, designed so x variables don’t get mistaken for multiplication12 · 6 = 72
/division: to divide something by something else150/5 = 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 brackets2 + [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 bracketsset: 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 is3 + 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 to7 = 4 + 3 ⇔ 4 = 7 – 3
therefore: some value is equal to another value meaning the opposite will also be equala = 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.

SymbolName and MeaningExample Problem
xvariable: an unknown value that needs to be found, other letters from the alphabet can be used as well2x = 4
2/2x = 4/2
x = 2
proportional: proportional toƒ(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 number4! = 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(x-1)
 Δdelta: change or difference Δt = t1 – t0
 Σsigma: summation, a sum of all values in a range of series Σxi = x1 + x2 + … + xn
ee constant: also known as Euler’s number, e = 2.718281828…e = lim(1 + 1/x)x, x → ∞
 γEuler-Mascheroni constant: a constant number, γ = 0.527721566…
gamma=lim_(n->infty)(sum_(k=1)^(n)1/k-lnn)
=lim_(n->infty)(H_n-lnn),
 φgolden 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 Euler-Mascheroni 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.

SymbolName and MeaningExample Problem
[ ]brackets: matrix of numbers⌈6 4 24⌉
⌊1 -9  8⌋
A⊗Btensor product: the most general bilineral operation, used for matrices and other algebraic equationsV⊗W := F(V ⋅ W)/R
ATtranspose: matrix transpose(AT)ij = (A)ji
AHermitian matrix: matrix conjugate transpose(A)ij = (̅A)ji
A-1inverse matrix: the reciprocal of a matrixA A-1 = I
rank(A)matrix rank: the rank of the matrix Arank (A) = 3
dim(U)dimension: a dimension of the matrix Arank (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.