My Math Land: Mathematical symbols- do u know these abbreviations?

Monday, January 27, 2014

Mathematical symbols- do u know these abbreviations?

Today lets learn about math symbols!!

Some of them may be really easy, but just bear with them!

Symbol in HTML	Symbol in $T E X$	Name	Explanation	Examples
		Read as
		Category
=	$=$	equality is equal to; equals everywhere	$x = y$ means $x$ and $y$ represent the same thing or value.	$2 = 2$ $1 + 1 = 2$
≠	$\ne$	inequality is not equal to; does not equal everywhere	$x \ne y$ means that $x$ and $y$ do not represent the same thing or value. (The forms !=, /= or <> are generally used in programming languages where ease of typing and use of ASCII text is preferred.)	$2 + 2 \ne 5$
< >	$<$ $>$	strict inequality is less than, is greater than order theory	$x < y$ means $x$ is less than $y$ . $x > y$ means $x$ is greater than $y$ .	$3 < 4$ $5 > 4$
< >	$<$ $>$	proper subgroup is a proper subgroup of group theory	$H < G$ means $H$ is a proper subgroup of $G$ .	$5Z < Z$ $A_3 < S_3$
≪ ≫	$\ll \!\,$ $\gg \!\,$	(very) strict inequality is much less than, is much greater than order theory	x ≪ y means x is much less than y. x ≫ y means x is much greater than y.	0.003 ≪ 1000000
≪ ≫	$\ll \!\,$ $\gg \!\,$	asymptotic comparison is of smaller order than, is of greater order than analytic number theory	f ≪ g means the growth of f is asymptotically bounded by g. (This is I. M. Vinogradov's notation. Another notation is the Big O notation, which looks like f = O(g).)	x ≪ e^x
≤ ≥	$\le \!\,$ $\ge$	inequality is less than or equal to, is greater than or equal to order theory	x ≤ y means x is less than or equal to y. x ≥ y means x is greater than or equal to y. (The forms <= and >= are generally used in programming languages, where ease of typing and use of ASCII text is preferred.)	3 ≤ 4 and 5 ≤ 5 5 ≥ 4 and 5 ≥ 5
		subgroup is a subgroup of group theory	H ≤ G means H is a subgroup of G.	Z ≤ Z A₃ ≤ S₃
		reduction is reducible to computational complexity theory	A ≤ B means the problem A can be reduced to the problem B. Subscripts can be added to the ≤ to indicate what kind of reduction.	If $\exists f \in F \mbox{ . } \forall x \in \mathbb{N} \mbox{ . } x \in A \Leftrightarrow f(x) \in B$ then $A \leq_{F} B$
≦ ≧	$\leqq \!\,$ $\geqq \!\,$	congruence relation ...is less than ... is greater than... modular arithmetic	7k ≡ 28 (mod 2) is only true if k is an even integer. Assume that the problem requires k to be non-negative; the domain is defined as 0 ≦ k ≦ ∞.	10a ≡ 5 (mod 5) for 1 ≦ a ≦ 10
≦ ≧	$\leqq \!\,$ $\geqq \!\,$	vector inequality ... is less than or equal... is greater than or equal... order theory	x ≦ y means that each component of vector x is less than or equal to each corresponding component of vector y. x ≧ y means that each component of vector x is greater than or equal to each corresponding component of vector y. It is important to note that x ≦ y remains true if every element is equal. However, if the operator is changed, x ≤ y is true if and only if x ≠ y is also true.
≺	$\prec \!\,$	Karp reduction is Karp reducible to; is polynomial-time many-one reducible to computational complexity theory	L₁ ≺ L₂ means that the problem L₁ is Karp reducible to L₂.^[1]	If L₁ ≺ L₂ and L₂ ∈ P, then L₁ ∈ P.
∝	$\propto \!\,$	proportionality is proportional to; varies as everywhere	y ∝ x means that y = kx for some constant k.	if y = 2x, then y ∝ x.
∝	$\propto \!\,$	Karp reduction^[2] is Karp reducible to; is polynomial-time many-one reducible to computational complexity theory	A ∝ B means the problem A can be polynomially reduced to the problem B.	If L₁ ∝ L₂ and L₂ ∈ P, then L₁ ∈ P.

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)