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Shoelace knot – commonly used for tying shoelaces and bow-ties; Shroud knot – a multi-strand bend knot used to join two ends of laid (or twisted) rope together; Siberian hitch – used to attach a rope to an object; Simple knot – (four-in-hand knot) a method of tying a necktie; Simple Simon over – used for joining two lines
In the ordinary sense of the word, the unknot is not "knotted" at all. The simplest nontrivial knots are the trefoil knot (3 1 in the table), the figure-eight knot (4 1) and the cinquefoil knot (5 1). [5] Several knots, linked or tangled together, are called links. Knots are links with a single component.
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". For example, > is normally printed "x such that > ". 2.
An example is 1*2 −3 2. The 1* denotes the only 1-vertex basic polyhedron. The 2 −3 2 is a sequence describing the continued fraction associated to a rational tangle. One inserts this tangle at the vertex of the basic polyhedron 1*. A more complicated example is 8*3.1.2 0.1.1.1.1.1 Here again 8* refers to a basic polyhedron with 8 vertices.
A result is called "deep" if its proof requires concepts and methods that are advanced beyond the concepts needed to formulate the result. For example, the prime number theorem — originally proved using techniques of complex analysis — was once thought to be a deep result until elementary proofs were found. [1]
Water knot (also known as Tape Knot, Double Overhand Bend, Ring Bend): The Water knot is useful to tie together two ends of ropes. Often used with webbing. Binding Strangle knot: The Strangle knot is a simple binding knot. It forms both sides of a Double fisherman's knot, and is also used to back up loop knots and both ends of bends.
For example, a co-dimension 2 link in 3-dimensional space is a subspace of 3-dimensional Euclidean space (or often the 3-sphere) whose connected components are homeomorphic to circles. The simplest nontrivial example of a link with more than one component is called the Hopf link , which consists of two circles (or unknots ) linked together once.
Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology. Axiom of extensionality; Axiom of empty set; Axiom of pairing; Axiom of union; Axiom of infinity; Axiom schema of replacement; Axiom of power set ...