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List of mathematical symbols
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The following list contains some of the most notable symbols in mathematics. Please note that these symbols may have alternate meanings in different contexts.
Symbol  Name  Read as  Meaning  Example 

=

equality  equals, is equal to  If x=y, x and y represent the same value or thing.  2+3=5 
≡

definition  is defined as  If x≡y, x is defined as another name of y  (a+b)^{2}≡a^{2}+2ab+b^{2} 
≈

approximately equal  is approximately equal to  If x≈y, x and y are almost equal.  √2≈1.41 
≠

inequation  does not equal, is not equal to  If x≠y, x and y do not represent the same value or thing.  1+1≠3 
<

strict inequality

is less than  If x<y, x is less than y.  4<5 
>

is greater than  If x>y, x is greater than y.  3>2  
≪

is much less than  If x≪y, x is much less than y.  1≪999999999  
≫

is much greater than  If x≫y, x is much greater than y.  88979808≫0.001  
≤

inequality

is less than or equal to  If x≤y, x is less than or equal to y.  5≤6 and 5≤5 
≥

is greater than or equal to  If x≥y, x is greater than or equal to y.  2≥1 and 2≥2  
∝

proportionality  is proportional to  If x∝y, then y=kx for some constant k.  If y=4x then y∝x and x∝y 
+

addition  plus  x+y is the sum of x and y.  2+3=5 


subtraction  minus  xy is the subtraction of y from x  53=2 
×

multiplication  times  x×y is the multiplication of x by y  4×5=20 
·

x·y is the multiplication of x by y  4·5=20  
÷

division  divided by  x÷y or x/y is the division of x by y  20÷4=5 and 20/4=5 
/

20/4=5  
±

plusminus  plus or minus  x±y means both x+y and xy  The equation 3±√9 has two solutions, 0 and 6. 
∓

minusplus  minus or plus  4±(3∓5) means both 4+(35) and 4(3+5)  6∓(1±3)=2 or 4 
√

square root  square root  √x is a number whose square is x.  √4=2 or 2 
∑

summation  sum over … from … to … of, sigma  [math]\sum_{k=1}^{n}{x_k}[/math] is the same as x_{1}+x_{2}+x_{3}+x_{k}  [math]\sum_{k=1}^{5}{k+2}=3+4+5+6+7=25[/math] 
∏

multiplication  product over … from … to … of  [math]\prod_{k=1}^{n}{x_k}[/math] is the same as x_{1}×x_{2}×x_{3}×x_{k}  [math]\prod_{k=1}^{5}{k}[/math]=1×2×3×4×5=120 
!

factorial  factorial  n! is the product 1×2×3...×n  5!=1×2×3×4×5=120 
⇒

material implication  implies  A⇒B means that if A is true, B must also be true, but if A is false, B is unknown.  x=3⇒x^{2}=9, but x^{2}=9⇒x=3 is false, because x could also be 3. 
⇔

material equivalence  if and only if  If A is true, B is true and if A is false, B is false.  x=y+1⇔x1=y 
…

absolute value  absolute value of  x is the distance along the real line (or across the complex plane) between x and zero  5=5 and 5=5 


parallel  is parallel to  If AB then A and B are parallel  
⊥

perpendicular  is perpendicular to  If A⊥B then A is perpendicular to B  
≅

congruence  is congruent to  If A≅B then shape A is congruent to shape B (has the same measurements)  
φ

golden ratio  golden ratio  The golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887.  
∞

infinity  infinity  ∞ is a number greater than every real number.  
∈

set membership  is an element of  a∈S means that a is an element of the set S  3.5∈ℝ, 1∈ℕ, 1+i∈ℂ 
∉

is not an element of  a∉S means that a is not an element of the set S  2.1∉ℕ, 1+i∉ℝ  
{,}

Set brackets  the set of  {a,b,c} is the set consisting of a, b, and c  ℕ={0,1,2,3,4,5...} 
ℕ

Natural numbers  N  ℕ denotes the set of natural numbers {0,1,2,3,4,5...}  
ℤ

Integers  Z  ℤ denotes the set of integers (3,2,1,0,1,2,3...)  
ℚ

Rational numbers  Q  ℚ denotes the set of rational numbers (numbers that can be written as a fraction a/b where a∈ℤ, b∈ℕ)  8.323∈ℚ, 7∈ℚ, π∉ℚ 
ℝ

Real numbers  R  ℝ denotes the set of real numbers  π∈ℝ, 7∈ℝ, √(1)∉ℝ 
ℂ

Complex numbers  C  ℂ denotes the set of complex numbers  √(1)∈ℂ 
x̄

Mean  bar, overbar  x̄ is the mean (average) of x_{i}  if x={1,2,3} then x̄=2 
x̄

complex conjugate  the complex conjugate of x  If x=a + bi, then x̄=a  bi where i=√(1)  x=4 + 5.3i, x̄=4  5.3i 
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