Mathematics
Mathematics is in General Things.
Culture, General Things, Mathematics, Numbers
Real Numbers
Real Numbers can be either Algebraic Numbers or Transcendental Number.
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
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
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
PI is the ratio of diameter and circumference of a circle. It is a Transcendental Number.
Culture, General Things, Mathematics, Series
Fibonacci Series
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.