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2. Inversive geometry - Wikipedia

   en.wikipedia.org/wiki/Inversive_geometry

   Circles intersect their inverses, if any, on the reference circle. In the SVG file, click or hover over a circle to highlight it. Inversion of a line is a circle containing the center of inversion; or it is the line itself if it contains the center; Inversion of a circle is another circle; or it is a line if the original circle contains the center

3. Set inversion - Wikipedia

   en.wikipedia.org/wiki/Set_inversion

   In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f −1 (Y ) = {x ∈ R n | f(x) ∈ Y }. It can also be viewed as the problem of describing the solution set of the quantified constraint "Y(f (x))", where Y( y) is a constraint, e.g. an inequality, describing the set Y.

4. Inversion (discrete mathematics) - Wikipedia

   en.wikipedia.org/wiki/Inversion_(discrete...

   An inversion may be denoted by the pair of places (2, 4) or the pair of elements (5, 2). The inversions of this permutation using element-based notation are: (3, 1), (3, 2), (5, 1), (5, 2), and (5,4). In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order.

5. Parity of a permutation - Wikipedia

   en.wikipedia.org/wiki/Parity_of_a_permutation

   For the n = j − i − 1 elements within the interval (i, j), assume v i of them form inversions with i and v j of them form inversions with j. If i and j are swapped, those v i inversions with i are gone, but n − v i inversions are formed. The count of inversions i gained is thus n − 2v i, which has the same parity as n.

6. Interval (mathematics) - Wikipedia

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

   The Encyclopedia of Mathematics [7] defines interval (without a qualifier) to exclude both endpoints (i.e., open interval) and segment to include both endpoints (i.e., closed interval), while Rudin's Principles of Mathematical Analysis [8] calls sets of the form [a, b] intervals and sets of the form (a, b) segments throughout.

7. Involution (mathematics) - Wikipedia

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

   Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...