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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]
However, Square brackets, as in = 3, are sometimes used to denote the floor function, which rounds a real number down to the next integer. Conversely, some authors use outwards pointing square brackets to denote the ceiling function, as in ]π[ = 4. Braces, as in {π} < 1 / 7, may denote the fractional part of a real number.
TemplateData for Ceil. Displays the parameter wrapped in ceiling symbols. This template is for display, not calculation. ... The operand of the ceiling function. Example
Functional notation: if the first is the name (symbol) of a function, denotes the value of the function applied to the expression between the parentheses; for example, (), (+). In the case of a multivariate function , the parentheses contain several expressions separated by commas, such as f ( x , y ) {\displaystyle f(x,y)} .
For example, 1.4 rounded is 1, the floor of 1.4 is 1, the ceiling of 1.4 is 2. 1.6 rounded is 2, the floor of 1.6 is 1, the ceiling of 1.6 is 2. So the floor of a fraction is always down; the ceiling of a fraction is always up; rounding can be up or down depending upon
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.
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However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the function rounds towards negative infinity. For a given number x ∈ R − {\displaystyle x\in \mathbb {R} _{-}} , the function ceil {\displaystyle \operatorname {ceil} } is used instead