# Category:Euler's Number

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This category contains results about **Euler's number $e$**.

Definitions specific to this category can be found in Definitions/Euler's Number.

The sequence $\sequence {x_n}$ defined as $x_n = \paren {1 + \dfrac 1 n}^n$ converges to a limit as $n$ increases without bound.

That limit is called **Euler's Number** and is denoted $e$.

## Subcategories

This category has the following 6 subcategories, out of 6 total.

## Pages in category "Euler's Number"

The following 44 pages are in this category, out of 44 total.

### A

### C

### E

- Equivalence of Definitions of Euler's Number
- Euler's Identity
- Euler's Number as Limit of 1 + Reciprocal of n to nth Power
- Euler's Number as Limit of n over nth Root of n Factorial
- Euler's Number as Sum of Egyptian Fractions
- Euler's Number is Irrational
- Euler's Number is Transcendental
- Euler's Number to Power of Euler-Mascheroni Constant
- Euler's Number to Power of its Negative
- Euler's Number to Power of its Reciprocal
- Euler's Number to Power of Itself
- Euler's Number to Power of Minus Euler-Mascheroni Constant
- Euler's Number: Limit of Sequence implies Base of Logarithm
- Euler's Number: Limit of Sequence implies Limit of Series
- Euler's Number: Limit of Sequence implies Limit of Series/Proof 1
- Euler's Number: Limit of Sequence implies Limit of Series/Proof 2

### I

### P

### S

- Schanuel's Conjecture Implies Algebraic Independence of Pi and Euler's Number over the Rationals
- Schanuel's Conjecture Implies Transcendence of 2 to the power of Euler's Number
- Schanuel's Conjecture Implies Transcendence of 2 to the power of Euler's Number/Lemma
- Schanuel's Conjecture Implies Transcendence of Euler's Number to the power of Euler's Number
- Schanuel's Conjecture Implies Transcendence of Pi by Euler's Number
- Schanuel's Conjecture Implies Transcendence of Pi plus Euler's Number
- Schanuel's Conjecture Implies Transcendence of Pi to the power of Euler's Number
- Schanuel's Conjecture Implies Transcendence of Pi to the power of Euler's Number/Lemma
- Square Root of Euler's Number
- Square Root/Examples/Euler's Number
- Steiner's Calculus Problem