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In calculus, a real-valued function of a real variable or real function is a partial function from the set of the real numbers to itself. Given a real function f : x ↦ f ( x ) {\displaystyle f:x\mapsto f(x)} its multiplicative inverse x ↦ 1 / f ( x ) {\displaystyle x\mapsto 1/f(x)} is also a real function.
In mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation.Algebraic functions are often algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).
Real algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and ordered rings (in particular real closed fields ) and their applications to the study of positive polynomials and sums-of-squares of polynomials .
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
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