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In the context of proofs, this phrase is often seen in induction arguments when passing from the base case to the induction step, and similarly, in the definition of sequences whose first few terms are exhibited as examples of the formula giving every term of the sequence. necessary and sufficient
A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor. It can be fully reduced to lowest terms if both are divided by their greatest common divisor. [5] In order to find the greatest common divisor, the Euclidean algorithm or prime factorization can be used. The Euclidean algorithm is ...
This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology. This list is limited to abbreviations of two or more letters (excluding number sets). The capitalization of some of these abbreviations is not standardized – different authors might use different capitalizations.
For example, is not in lowest terms because both 3 and 9 can be exactly divided by 3. In contrast, is in lowest terms—the only positive integer that goes into both 3 and 8 evenly is 1. Using these rules, we can show that 5 / 10 = 1 / 2 = 10 / 20 = 50 / 100 , for example. As another example, since the greatest ...
When the meaning depends on the syntax, a symbol may have different entries depending on the syntax. For summarizing the syntax in the entry name, the symbol is used for representing the neighboring parts of a formula that contains the symbol. See § Brackets for examples of use. Most symbols have two printed versions.
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. This is a listing of articles which explain some of these functions in more detail.
For example, the polynomial +, which can also be written as +, has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.