Mathematics is in General Things.
Real Numbers can be either Algebraic Numbers or Transcendental Number.
Transcendental Number are numbers which are non-algebraic. They transcend Algebraic Numbers hence the name.
Real Numbers can be either Algebraic Numbers or Transcendental Number.
Natural Logarithm of 2. Is the logarithm of 2 to the base of e. It is usually written as ln2. It is a Transcendental Number.
The Alternating Harmonic Series: SUM(1,INFINITY) ( (-1)**(N+1) ) / N = 1 (1/2) + (1/3) (1/4) + (1/5) (1/6) + ....
Or Binary Rising Constant Factorial: SUM(1,INFINITY) 1 / ( ( 2**N ) *N) = 1/2 + 1/8 + 1/24 + 1/64 + 1/160 + 1/384 + 1/896 + ....
Or SUM(0,INFINITY) 1 / ( ( 2N + 1 ) * ( 2N + 2 ) ) = 1 / ( 4N**2 + 6N + 2 ) = 1/2 + 1/12 + 1/30 + 1/56 + 1/90 + 1/132 + 1/182 + 1/240 + ....
e. Euler's Number is 2.718254. It is usually written as 'e'. It is a Transcendental Number.
Euler's Number is the number to which compounding, as in compount interest, converges.
For example, if interest is paid at 100% then after one year £1 becomes £2.
If the interest is charged at 50% twice then the interest will be ( 1 * 1.5 ) * 1.5 = 1.5**2 = 2.25
If the interest is charged at 25% four times then the interest will be ( ( ( ( 1 * 1.25 ) * 1.25 ) * 1.25 ) * 1.25 )= 1.25**4 = 2.44
If the interest is charged at 8.33% twelve times then the interest will be 1.0833**12 = 2.612
If the interest is charged at 4.2% twenty-four times year then the interest will be ( 1.042**4 ) = 2.67
If the interest is charged at 0.1% one thousand times then the interest will be ( 1.001**1000 ) = 2.72
If the interest is charged at an infinite number of times then the interest will be ( 1.00/∞ )**∞ = 2.718254... which is Euler's number.
Euler's Number is the sum of the infinite series ( 1 / n! ) ie 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 + 1/720 + 1/5040 .... = 2.718281828.
Natural Logarithm of 2. Is the logarithm of 2 to the base of e. It is usually written as ln2. It is a Transcendental Number.
The Alternating Harmonic Series: SUM(1,INFINITY) ( (-1)**(N+1) ) / N = 1 (1/2) + (1/3) (1/4) + (1/5) (1/6) + ....
Or Binary Rising Constant Factorial: SUM(1,INFINITY) 1 / ( ( 2**N ) *N) = 1/2 + 1/8 + 1/24 + 1/64 + 1/160 + 1/384 + 1/896 + ....
Or SUM(0,INFINITY) 1 / ( ( 2N + 1 ) * ( 2N + 2 ) ) = 1 / ( 4N**2 + 6N + 2 ) = 1/2 + 1/12 + 1/30 + 1/56 + 1/90 + 1/132 + 1/182 + 1/240 + ....
PI is the ratio of diameter and circumference of a circle. It is a Transcendental Number.
Fibonacci Series. The series that starts with 0 and 1. Some mathematicians suggest it starts with 1 and 1. The next term in the series is the sum of its previous two terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.