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A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e. surjective). Not translatable (without circumlocutions) to some languages other than English.
Sets can themselves be elements. For example, consider the set = {,, {,}}. The elements of B are not 1, 2, 3, and 4. Rather, there are only three elements of B, namely the numbers 1 and 2, and the set {,}. The elements of a set can be anything.
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
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".
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [ 2 ] [ 3 ] Thus, in the expression 1 + 2 × 3 , the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7 , and not (1 + 2) × 3 = 9 .
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The rationale behind this is that it enables design and usage of special mathematical characters that include all necessary properties to differentiate from other alphanumerics, e.g. in mathematics an italic "𝐴" can have a different meaning from a roman letter "A".
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