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ap-a is an integral multiple of p for every prime number p and integer a.
What is Fermat's little theorem?
This theorem/law allows us to say that if an apple is red, then an apple is not not red.
What is double negation?
You would type '\varnothing' in LaTeX to get the symbol used for this object.
What is empty set?
This number is the smallest prime number whose digits are themselves prime numbers.
What is 23?
The _____'s sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cuts.
What is "lazy caterer"?
___'s basis theorem states that a polynomial ring over a Noetherian ring is Noetherian.
Who is Hilbert?
This lemma allows us to "glue" together continuous functions on closed sets to create a continuous function on the whole space.
What is Pasting/gluing lemma?
This type of discontinuity of a function is a point at which the limit of the function does not exist.
What is essential?
This is the slope of the line consisting of all points (x,f(x)) given by the equation x=3.
What is undefined?
The father and mother of a child have the same age and are currently 21 years older than their child. In six years, the mother will be 5 times the age of the child. This is the current location of the father.
What is "with the mother"?
The ____ theorem is a fundamental result of analysis giving necessary and sufficient conditions to decide whether a sequence of a given family of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence.
What is Arzelà–Ascoli?
This theorem deals with the intersection of a type of collections of closed sets in R.
What is Nested interval theorem/Cantor intersection theorem?
This variable takes the value 0 for a circle, 1 for a parabola, is more than 1 for a hyperbola and is in between 0 and 1 for an ellipse.
What is eccentricity?
This many regular pentagons make up a dodecahedron.
What is twelve?
Beware! This set (of a topological space X) is the Stone-Cech compactification of X minus the set X.
What is Corona?
In probability theory, ___'s inequality guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean.
Who is Chebyshev?
This question asks to determine the plane figure of the largest possible area whose boundary has a specified length.
What is the isoperimetric problem?
Every closed 3-dimensional manifold can be cut into pieces that are geometrizable, by the geometrization conjecture, and there are this many such geometries.
What is eight?
The _____ of the topological space X is a compact Hausdorff space βX together with a continuous map i: X → βX that has the following universal property: any continuous map f:X → K, where K is a compact Hausdorff space, extends uniquely to a continuous map βf : βX → K, i.e. (βf)iX = f.
What is Stone-Cech compactification?
This book by Fine and Rosenberger is named after a basic but important theorem in algebra and contains 8 proofs for the same.
What is the Fundamental Theorem of Algebra?
In combinatorial set theory, the ___ theorem is a basic result, extending Ramsey's theorem to uncountable sets.
What is Erdős–Rado?
In geometry, this theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously.
What is Killing-Hopf?