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2. Glossary of calculus - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_calculus

   [57] [58] In general, a common fraction is said to be a proper fraction if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. [59] [60] It is said to be an improper fraction, or sometimes top-heavy fraction, [61] if the absolute value of the fraction is greater than or ...

3. Equality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Equality_(mathematics)

   The term extensionality, as used in 'Axiom of Extensionality' has its roots in logic. An intensional definition describes the necessary and sufficient conditions for a term to apply to an object. For example: "An even number is an integer which is divisible by 2." An extensional definition instead lists all objects where the term applies.

4. Field (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Field_(mathematics)

   An equivalent, and more succinct, definition is: a field has two commutative operations, called addition and multiplication; it is a group under addition with 0 as the additive identity; the nonzero elements form a group under multiplication with 1 as the multiplicative identity; and multiplication distributes over addition.

5. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   In a fraction, the number of equal parts being described is the numerator (from Latin: numerātor, "counter" or "numberer"), and the type or variety of the parts is the denominator (from Latin: dēnōminātor, "thing that names or designates"). [2] [3] As an example, the fraction ⁠ 8 / 5 ⁠ amounts to eight parts, each of which is of the ...

6. Glossary of mathematical symbols - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   2. Denotes the additive inverse and is read as minus, the negative of, or the opposite of; for example, –2. 3. Also used in place of \ for denoting the set-theoretic complement; see \ in § Set theory. × (multiplication sign) 1. In elementary arithmetic, denotes multiplication, and is read as times; for example, 3 × 2. 2.

7. Irreducible fraction - Wikipedia

   en.wikipedia.org/wiki/Irreducible_fraction

   For example, ⁠ 1 / 4 ⁠, ⁠ 5 / 6 ⁠, and ⁠ −101 / 100 ⁠ are all irreducible fractions. On the other hand, ⁠ 2 / 4 ⁠ is reducible since it is equal in value to ⁠ 1 / 2 ⁠, and the numerator of ⁠ 1 / 2 ⁠ is less than the numerator of ⁠ 2 / 4 ⁠. A fraction that is reducible can be reduced by dividing both the numerator ...

8. Relation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Relation_(mathematics)

   As an example, "is less than" is a relation on the set of natural numbers; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3), and likewise between 3 and 4 (denoted as 3 < 4), but not between the values 3 and 1 nor between 4 and 4, that is, 3 < 1 and 4 < 4 both evaluate to false.

9. Mediant (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Mediant_(mathematics)

   However, if the fraction 1/1 is replaced by the fraction 2/2, which is an equivalent fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions may be required to be reduced to lowest terms, thereby selecting unique representatives from the ...