| align=intersected with; intersect |  |  |  |  |  |
| align=set theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div> <math>\Delta</math> </div> | symmetric difference | <math> A\Delta B</math> means the set of elements in exactly one of *A* or *B*. | {1,5,6,8} <math>\Delta</math> {2,5,8} = {1,2,6} |  |  |
| align=symmetric difference |  |  |  |  |  |
| align=set theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div></div> | set-theoretic complement | *A*&nbsp;&nbsp;*B* means the set that contains all those elements of *A* that are not in *B*.  
− can also be used for set-theoretic complement as described above. | {1,2,3,4}&nbsp;&nbsp;{3,4,5,6}&nbsp;= {1,2} |  |  |
| align=minus; without |  |  |  |  |  |
| align=set theory |  |  |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>(&nbsp;)</div> | function application | *f*(*x*) means the value of the function *f* at the element *x*. | If *f*(*x*)&nbsp;:= *x*<sup>2</sup>, then *f*(3)&nbsp;= 3<sup>2</sup>&nbsp;= 9. |  |  |
| align=of |  |  |  |  |  |
| align=set theory |  |  |  |  |  |
| precedence grouping | Perform the operations inside the parentheses first. | (8/4)/2&nbsp;= 2/2&nbsp;= 1, but 8/(4/2)&nbsp;= 8/2&nbsp;= 4. |  |  |  |
| align=parentheses |  |  |  |  |  |
| align=everywhere |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>*f*:*X*→*Y*</div> | function arrow | *f*:&nbsp;*X*&nbsp;→ *Y* means the function *f* maps the set *X* into the set *Y*. | Let *f*:&nbsp;&nbsp;→&nbsp; be defined by *f*(*x*)&nbsp;:= *x*<sup>2</sup>. |  |  |
| align=from … to |  |  |  |  |  |
| align=set theory,type theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div><small>o</small></div> | சார்புகளின் தொகுப்பு | *f*<small>o</small>*g* is the function, such that (*f*<small>o</small>*g*)(*x*) = *f*(*g*(*x*)). | if *f*(*x*) := 2*x*, and *g*(*x*) := *x* + 3, then (*f*<small>o</small>*g*)(*x*) = 2(*x* + 3). |  |  |
| align=composed with |  |  |  |  |  |
| align=set theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>  
**N**</div> | இயற்கை எண்கள் | **N** means {&nbsp;1, 2, 3, …}, but see the article on natural numbers for a different convention. | &nbsp;: *a*&nbsp;∈ , *a*&nbsp;≠ 0} |  |  |
| align=N |  |  |  |  |  |
| align=எண்s |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>  
**Z**</div> | நிறை எண்கள் | means {..., −3, −2, −1, 0, 1, 2, 3, …} and <sup>+</sup> means {1, 2, 3, …}&nbsp;= . | &nbsp;= {*p*,&nbsp;-*p*&nbsp;: *p*&nbsp;∈ }&nbsp;∪&nbsp;{0} |  |  |
| align=Z |  |  |  |  |  |
| align=எண்s |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>  
**Q**</div> | விகிதமுறு எண்கள் | means {*p*/*q*&nbsp;: *p*&nbsp;∈&nbsp;, *q*&nbsp;∈&nbsp;}. | 3.14000...&nbsp;∈  
π&nbsp; |  |  |
| align=Q |  |  |  |  |  |
| align=எண்s |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>  
**R**</div> | மெய்யெண்s | ℝ means the set of real numbers. | π&nbsp;∈  
√(−1)&nbsp; |  |  |
| align=R |  |  |  |  |  |
| align=எண்s |  |  |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>  
**C**</div> | சிக்கலெண்s | means {*a*&nbsp;+&nbsp;*b*&nbsp;***i***&nbsp;: *a*,*b*&nbsp;∈&nbsp;}. | ***i***&nbsp;= √(−1)&nbsp;∈ |  |  |
| C'' |  |  |  |  |  |
| align=எண்s |  |  |  |  |  |
| arbitrary constant | *C* can be any number, most likely unknown; usually occurs when calculating antiderivatives. | if *f(x)* = 6*x*² + 4*x*, then *F(x)* = 2*x*³ + 2*x*² + *C*, where *F'(x)* = *f(x)* |  |  |  |
| align=C |  |  |  |  |  |
| align=தொகையீடு |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>  
**K**</div> | real or சிக்கலெண்s | **K** means the statement holds substituting **K** for **R** and also for **C**. | : <math>x^2\in\mathbb{C}\,\forall x\in \mathbb{K}</math>
because
: <math>x^2\in\mathbb{C}\,\forall x\in \mathbb{R}</math>
and
:<math>x^2\in\mathbb{C}\,\forall x\in \mathbb{C}</math>. |  |  |
| align=K |  |  |  |  |  |
| align=நேரியல் இயற்கணிதம் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>∞</div> | எண்ணிலி | ∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits. | } = \infty</math> |  |  |
| align=எண்ணிலி |  |  |  |  |  |
| align=எண்s |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>…</div> | norm | &nbsp;*x*&nbsp; is the norm of the element *x* of a normed vector space. | &nbsp;*x*&nbsp; + *y*&nbsp; ≤&nbsp; &nbsp;*x*&nbsp;&nbsp; +&nbsp; &nbsp;*y*&nbsp; |  |  |
| align=norm of  
length of |  |  |  |  |  |
| align= நேரியல் இயற்கணிதம் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>∑</div> | summation | <math>\sum_{k=1}^{n}{a_k}</math> means *a*<sub>1</sub>&nbsp;+ *a*<sub>2</sub>&nbsp;+ …&nbsp;+ *a*<sub>*n*</sub>. | <math>\sum_{k=1}^{4}{k^2}</math> = 1<sup>2</sup>&nbsp;+ 2<sup>2</sup>&nbsp;+ 3<sup>2</sup>&nbsp;+ 4<sup>2</sup>&nbsp;
::= 1&nbsp;+ 4&nbsp;+ 9&nbsp;+ 16&nbsp;= 30 |  |  |
| align=sum over … from … to … of |  |  |  |  |  |
| align=எண்கணிதம் |  |  |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>∏</div> | product | <math>\prod_{k=1}^na_k</math> means *a*<sub>1</sub>*a*<sub>2</sub>···*a*<sub>*n*</sub>. | <math>\prod_{k=1}^4(k+2)</math> = (1+2)(2+2)(3+2)(4+2)
::= 3&nbsp;× 4&nbsp;× 5&nbsp;× 6&nbsp;= 360 |  |  |
| align=product over … from … to … of |  |  |  |  |  |
| align=எண்கணிதம் |  |  |  |  |  |
| கார்ட்டீசியன் பெருக்கற்பலன் | <math>\prod_{i=0}^{n}{Y_i}</math> means the set of all (n+1)-tuples
::(*y*<sub>0</sub>, …, *y*<sub>*n*</sub>). | <math>\prod_{n=1}^{3}{\mathbb{R}} = \mathbb{R}\times\mathbb{R}\times\mathbb{R} = \mathbb{R}^3</math> |  |  |  |
| align=the Cartesian product of; the direct product of |  |  |  |  |  |
| align=set theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div></div> | coproduct |  |  |  |  |
| align=coproduct over … from … to … of |  |  |  |  |  |
| align=category theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>′  
<sup>•</sup></div> | வகையிடல் | *f*&nbsp;′(*x*) is the derivative of the function *f* at the point *x*, i.e., the சாய்வு of the தொடுகோடு to *f* at *x*.  
The dot notation indicates a time derivative. That is <math>\dot{x}(t)=\frac{\partial}{\partial t}x(t)</math>. | If *f*(*x*)&nbsp;:=&nbsp;*x*<sup>2</sup>, then *f*&nbsp;′(*x*)&nbsp;=&nbsp;2*x* |  |  |
| align=… prime  
derivative of |  |  |  |  |  |
| align=நுண்கணிதம் |  |  |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>∫</div> | indefinite integral or antiderivative | ∫&nbsp;*f*(*x*)&nbsp;d*x* means a function whose derivative is *f*. | ∫*x*<sup>2</sup>&nbsp;d*x*&nbsp;= *x*<sup>3</sup>/3 + C |  |  |
| align=indefinite integral of  
the antiderivative of |  |  |  |  |  |
| align=நுண்கணிதம் |  |  |  |  |  |
| தொகையீடு | ∫<sub>*a*</sub><sup>*b*</sup>&nbsp;*f*(*x*)&nbsp;d*x* means the signed பரப்பளவு between the *x*-axis and the graph of the function *f* between *x*&nbsp;= *a* and *x*&nbsp;= *b*. | ∫<sub>0</sub><sup>*b*</sup>&nbsp;x<sup>2 </sup>&nbsp;d*x*&nbsp;= *b*<sup>3</sup>/3; |  |  |  |
| align=integral from … to … of … with respect to |  |  |  |  |  |
| align=நுண்கணிதம் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>∮</div> | contour integral or closed line integral | Similar to the integral, but used to denote a single integration over a closed curve or loop. It is sometimes used in physics texts involving equations regarding Gauss's Law, and while these formulas involve a closed surface integral, the representations describe only the first integration of the volume over the enclosing surface. Instances where the latter requires simultaneous double integration, the symbol would be more appropriate. A third related symbol is the closed volume integral, denoted by the symbol .
The contour integral can also frequently be found with a subscript capital letter *C*, ∮<sub>*C*</sub>, denoting that a closed loop integral is, in fact, around a contour *C*, or sometimes dually appropriately, a circle *C*. In representations of Gauss's Law, a subscript capital *S*, ∮<sub>*S*</sub>, is used to denote that the integration is over a closed surface. |  |  |  |