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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]
The service ceiling is the maximum altitude of an aircraft during normal operations. Specifically, it is the density altitude at which flying in a clean configuration , at the best rate of climb airspeed for that altitude and with all engines operating and producing maximum continuous power, will produce a given rate of climb.
This maximum altitude is known as the service ceiling (top limit line in the diagram), and is often quoted for aircraft performance. The area where the altitude for a given speed can no longer be increased at level flight is known as zero rate of climb and is caused by the lift of the aircraft getting smaller at higher altitudes, until it no ...
V x increases with altitude and V Y decreases with altitude until they converge at the airplane's absolute ceiling, the altitude above which the airplane cannot climb in steady flight. The Cessna 172 is a four-seat aircraft. At maximum weight it has a V Y of 75 kn (139 km/h) indicated airspeed [4] providing a rate of climb of 721 ft/min (3.66 m/s).
The above dyadic functions examples [left and right examples] (using the same / symbol, right example) demonstrate how Boolean values (0s and 1s) can be used as left arguments for the \ expand and / replicate functions to produce exactly opposite results.
Displays the parameter wrapped in ceiling symbols. This template is for display, not calculation. Template parameters [Edit template data] This template prefers inline formatting of parameters. Parameter Description Type Status Operand 1 The operand of the ceiling function Example π Line required Examples {{ceil|45.23}} → ⌈45.23⌉ {{ceil|''x''}} → ⌈ x ⌉ {{ceil|{{sfrac|2''a''|''b ...
the floor, ceiling and fractional part functions are idempotent; the real part function () of a complex number, is idempotent. the subgroup generated function from the power set of a group to itself is idempotent; the convex hull function from the power set of an affine space over the reals to itself is idempotent;
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