# Category:Mathematical proof

## Pages in category "Mathematical proof"

The following 136 pages are in this category, out of 136 total.

### A

### C

- Cohen-Macaulay graded ring/Positive characteristic/Parameter/Tight closure/Degree criterion/Inclusion/Fact/Proof
- Cohen-Macaulay ring/Positive characteristic/Cohomological criterion for tight closure/Fact/Proof
- Complex numbers/Field/Fact/Proof
- Complex numbers/Modulus/Rules/Fact/Proof
- Continuity in a point/K/Characterization/Fact/Proof
- Continuous Function/Primitive function exists/Fact/Proof
- Continuous function/R/Intermediate value theorem/0-version/Fact/Proof
- Continuous function/R/Intermediate value theorem/Fact/Proof
- Convergent power series/R/Taylor series/Coincidence/Fact/Proof
- Cosine/R/Addition theorem/Power series direct/Fact/Proof

### D

- Determinant/Field/Upper triangular matrix/Fact/Proof
- Determinant/Laplace expansion/Fact/Proof
- Determinant/Zero, linear dependent and rank property/Fact/Proof
- Differentiable function/D in R/Chain rule/Fact/Proof
- Differentiable function/D in R/Continuity in point/Fact/Proof
- Differentiable function/D in R/Inverse function/Fact/Proof
- Differentiable function/D in R/Linear approximation/Fact/Proof
- Differentiable function/D in R/Rules/Fact/Proof
- Differentiable function/D open in K/Chain rule/Fact/Proof
- Differentiable function/D open in K/Linear approximation/Fact/Proof
- Differentiable function/D open in K/Rules/Fact/Proof
- Differentiable function/Mean value theorem/Quotient version/Fact/Proof
- Differentiable functions/Mean value theorem/Fact/Proof

### E

- Endomorphism/Eigenvalue and characteristic polynomial/Fact/Proof
- Endomorphism/Eigenvectors/Linearly independent/Fact/Proof
- Endomorphism/Geometric and algebraic multiplicity/Fact/Proof
- Endomorphismus/Finite dimensional/Change of basis/Fact/Proof
- Exponential series/Real/Absolute convergence/Fact/Proof
- Exponential series/Real/Elementary properties/Fact/Proof
- Exponential series/Real/Functional equation/Fact/Proof

### F

- Field/Basic properties/Fact/Proof2
- Field/Binomi/Fact/Proof
- Field/Uniqueness of negative and inverse element/Fact/Proof2
- Finite field/Smooth projective curve/Vector bundle/Affineness and nonexistence of curves/Fact/Proof
- Finite field/Smooth projective curve/Vector bundle/Finite annihilation/Harder-Narasimhan-criterion/Fact/Proof
- Finite field/Smooth projective curve/Vector bundle/Strongly semistable degree 0/Trivializable/Fact/Proof
- Finite field/Smooth projective curve/Vector bundle/Strongly semistable degree nonnegative/Finite annihilation/Fact/Proof
- Forcing algebra/Primary ideal/Induced torsor/Fact/Proof
- Function/R/Limit/Epsilon/Rules/Fact/Proof
- Fundamental theorem of calculus/Riemann/Fact/Proof

### H

### I

### L

- Linear inhomogeneous system/Elimination/Echelon form/Fact/Proof
- Linear inhomogeneous system/Strictly triangular/Solution/Fact/Proof
- Linear mapping/Diagonalizable/Characterizations/Fact/Proof
- Linear mapping/Different eigenvalues/Diagonalizable/Fact/Proof
- Linear mapping/Eigenspace as kernel/Fact/Proof
- Linear mapping/Kernel/Injectivity/Fact/Proof
- Linear mapping/Matrix to basis/Injective and columns linearly independent/Fact/Proof
- Linear mapping/Matrix to basis/Several properties/Fact/Proof
- Linear mapping/Matrix/Composition/Fact/Proof2
- Linear system/Elimination lemma/Fact/Proof

### M

### N

### O

- Open subscheme/Affine and extended ideal/Finitely generated/Fact/Proof
- Ordered field/Bernoulli's inequality/Fact/Proof
- Ordered field/Convergent sequence/Bounded/Fact/Proof
- Ordered field/Convergent sequences/Rules/1/Fact/Proof
- Ordered field/Convergent sequences/Rules/2/Fact/Proof
- Ordered field/Elementary properties for inverses/Fact/Proof
- Ordered field/Sequence/Unique limit/Fact/Proof

### P

- Polynomial function/R/Continuous/Fact/Proof2
- Polynomial ring/Field/One variable/Euclidean division/Fact/Proof
- Polynomial ring/Field/Zero/Linear factor/Fact/Proof
- Polynomial ring/Field/Zeroes/Number/Fact/Proof
- Polynomial/K/Interpolation/Fact/Proof
- Power function/Positive base/Real exponent/Fact/Proof
- Prime factorization/Existence/Fact/Proof2
- Prime numbers/Infinity/Fact/Proof
- Primitive function/1 over 1- x^2/Fact/Proof
- Primitive function/Inverse function/Fact/Proof
- Projective curve/Vector bundle/Cohomology class/Finite annihilation and torsor/Fact/Proof

### R

- Rational function/R/Continuous/Fact/Proof
- Real cosine function/One zero between 0 and 2/Fact/Proof
- Real exponential function/Base/Derivative/Fact/Proof
- Real Exponential function/Continuity and image/Fact/Proof
- Real exponential function/Continuity and image/Fact/Proof
- Real exponential function/Derivative/Fact/Proof
- Real function/Continuity in a point/Characterization/Fact/Proof
- Real function/Continuous/Addition, multiplication, inverting/Fact/Proof
- Real function/Continuous/Composition/Fact/Proof
- Real function/Derivative zero/Constant/Fact/Proof
- Real function/Derivative/Monotonicity/Fact/Proof
- Real function/Extrema/Higher derivatives/Fact/Proof
- Real function/Local extremum/Differentiable/Derivative zero/Fact/Proof
- Real function/Open interval/Local extrema/Differentiable/Derivative zero/Fact/Proof
- Real function/Taylor formula/(n+1)-times continuously differentiable/Estimate for error/Fact/Proof
- Real function/Theorem of Rolle/Fact/Proof
- Real numbers/Bernoulli's inequality/Fact/Proof
- Real numbers/Bolzano Weierstraß/Fact/Proof
- Real numbers/Bounded monotonic increasing sequence/Cauchy sequence/Fact/Proof
- Real numbers/Convergent sequence/Bounded/Fact/Proof
- Real numbers/Convergent sequence/Cauchy sequence/Fact/Proof
- Real numbers/Convergent sequences/Rules/Fact/Proof
- Real numbers/kth root of real number/Intermediate value theorem/Fact/Proof
- Real numbers/Ordering axioms/Archimedean/Implications/Fact/Proof2
- Real numbers/Sequence/Bounded monotone/Converges/Fact/Proof
- Real numbers/Sequence/Unique limit/Fact/Proof
- Real numbers/Series converges/Summands/Null sequence/Fact/Proof
- Real numbers/Series/Cauchy-criterion/Fact/Proof
- Real positive number/Root/Unique existence/Fact/Proof
- Real power series/Infinitely often differentiable/Fact/Proof
- Real series/Absolute convergence and convergence/Fact/Proof
- Real series/Direct comparison test/Fact/Proof
- Real series/Ratio test/Fact/Proof
- Regular ring/Positive characteristic/Forcing algebra/Not inside/Local cohomology/Fact/Proof
- Regular ring/Positive characteristic/Tight closure trivial/Fact/Proof
- Riemann integrability/Elementary properties/Fact/Proof2

### S

- Sine and cosine/R/Properties of periodicity/Fact/Proof
- Sine and cosine/Real/Properties/Fact/Proof
- Square matrix/C/Trigonalizable/Fact/Proof
- Square root/2/Irrational/Fact/Proof
- Standard space/K^n/Dimension n/Fact/Proof
- System of linear equations/Set of variables/Equivalent system/Manipulations/Fact/Proof

### T

- Tangent/Cotangent/Derivative/Fact/Proof
- Tight closure/Does not commute with localization/Fact/Proof
- Tight closure/Localization/Geometric deformation over one-dimensional domain/Fact/Proof
- Tight closure/Monsky-quartic/Explicit non-inclusion/Fact/Proof
- Tight closure/Not plus closure/Dimension two/Standard-graded/Fact/Proof