# Category:Powers

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This category contains results about powers in the context of Algebra.

Definitions specific to this category can be found in Definitions/Powers.

## Subcategories

This category has the following 16 subcategories, out of 16 total.

### C

### E

### I

### L

### O

### P

### R

### S

### Z

## Pages in category "Powers"

The following 52 pages are in this category, out of 52 total.

### I

### N

### O

### P

- Positive Power Function on Non-negative Reals is Strictly Increasing
- Power Dominates Logarithm
- Power Function is Monotone over Rationals
- Power Function is Monotone/Rational Number
- Power Function is Strictly Increasing over Positive Reals/Natural Exponent
- Power Function on Base between Zero and One is Strictly Decreasing
- Power Function on Base between Zero and One Tends to One as Power Tends to Zero/Rational Number
- Power Function on Base Greater than One is Strictly Increasing
- Power Function on Base greater than One tends to One as Power tends to Zero/Rational Number
- Power Function on Base greater than One tends to One as Power tends to Zero/Rational Number/Lemma
- Power Function on Strictly Positive Base is Continuous
- Power Function on Strictly Positive Base is Continuous/Rational Power
- Power Function on Strictly Positive Base is Continuous/Real Power
- Power Function on Strictly Positive Base is Convex
- Power Function tends to One as Power tends to Zero/Rational Number
- Power Function to Rational Power permits Unique Continuous Extension
- Power is Well-Defined
- Power is Well-Defined/Integer
- Power is Well-Defined/Rational
- Power of Positive Real Number is Positive
- Power of Real Number between Zero and One is Bounded
- Power of Real Number greater than One is Unbounded Above
- Power of Ring Negative
- Power to Real Number by Decimal Expansion is Uniquely Defined
- Powers Drown Logarithms
- Powers Drown Logarithms/Corollary
- Prime Powers Differing by One
- Product of Indices of Real Number