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List of mathematical symbols
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Some Basic Mathematical Symbols
Please note that many of these symbols may have alternate meanings and may also differ from those used in computer science.
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 

