Fixed Point Theorem
If 
is a continuous function 
For All 
, then has a Fixed Point in 
.This can be proven by noting that
Since
is continuous, the Intermediate Value Theorem guarantees that there exists a 
such that
so there must exist a
such that 
so there must exist a Fixed Point
.See also Banach Fixed Point Theorem, Brouwer Fixed Point Theorem, Kakutani's Fixed Point Theorem,Lefshetz Fixed Point Formula, Lefshetz Trace Formula, Poincaré-Birkhoff Fixed PointTheorem, Schauder Fixed Point Theorem- Symmetric Tensor
- Symmetroid
- Symmetry
- Symmetry Group
- Symmetry Operation
- Symmetry Principle
- Symplectic Diffeomorphism
- Symplectic Form
- Symplectic Group
- Symplectic Manifold
- Symplectic Map
- Symplectomorphism
- Synclastic
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- Syracuse Algorithm
- Syracuse Problem
- System of Differential Equations
- System of Equations
- Syzygies Problem
- Syzygy
- Szilassi Polyhedron
- Szpiro's Conjecture
- Sárközy's Theorem