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For example: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".
A reference to a standard or choice-free presentation of some mathematical object (e.g., canonical map, canonical form, or canonical ordering). The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes.
One definition of a red-eye flight is one that is too short to allow a full night's sleep. An example would be those flights from Los Angeles to New York City—about five hours' flying time—that depart between 2100 and 0100 Pacific time, and arrive between 0500 and 0900 Eastern time.
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured.
Step 1 (red): construct a circle with center at P and some fixed radius r to create points A′ and B′ on the line AB, which will be equidistant from P. Step 2 (green): construct circles centered at A′ and B′ having radius r. P and Q will be the points of intersection of these two circles. Point Q is then the reflection of point P through ...
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There is no general consensus about the definition of mathematics or its epistemological status—that is, its place inside knowledge. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science.