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A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a Turing machine; the Feferman–Schütte ordinal Γ 0 [17] represents: the specific weight of substances; the lower incomplete gamma function; the third angle in a triangle, opposite the side c
The two points P and P ' (red) are antipodal because they are ends of a diameter PP ', a segment of the axis a (purple) passing through the sphere's center O (black). P and P ' are the poles of a great circle g (green) whose points are equidistant from each (with a central right angle).
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
When used in this way, the stronger notion (such as "strong antichain") is a technical term with a precisely defined meaning; the nature of the extra conditions cannot be derived from the definition of the weaker notion (such as "antichain"). sufficiently large, suitably small, sufficiently close
Thus these six ratios define six functions of θ, which are the trigonometric functions. In the following definitions, the hypotenuse is the length of the side opposite the right angle, opposite represents the side opposite the given angle θ, and adjacent represents the side between the angle θ and the right angle. [2] [3]
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of ...
For the angle α, the sine function gives the ratio of the length of the opposite side to the length of the hypotenuse.. To define the sine and cosine of an acute angle , start with a right triangle that contains an angle of measure ; in the accompanying figure, angle in a right triangle is the angle of interest.