Eighty-nine is a natural number before 90 and after 88, in the sequence of natural numbers. Written in the Indian-Arabic notation: 89; in Roman numerals, LXXIX.
Summary
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- 1 Arithmetic
- 1 Properties
- 2 Notations
- 2 Algebra
- 3 Mathematical analysis
- 4 Source
- 5 References
Arithmetic
Properties
- It’s an odd number
- is a rational prime number, the penultimate of two digits, in the decimal numbering system
- it is a prime of the form 4p + 1, therefore it is not a Gaussian prime.
- can be written as the sum of the squares of 8 and 5 respectively
- as a Gaussian integer 89 = (8 + 5i) (8-5i) = (5-8i) (5 + 8i)
Notations
- Binary 1011001
- Quaternary 1121
- Quinary 324
- Octal 131
- Duodecimal 75
- Hexadecimal 59
Algebra
- It is in the additive group Z of the integers, its opposite is -89
- belongs to the multiplicative group of the rational ones, its multiplicative inverse is 1/89
- it is in the body of real numbers, with infinite decimal writing 88,999 …
- is a complex number, compound Gaussian integer, algebraic number.
Mathematical analysis
- Using the absolute value function, if | x | = 89 then x = 89 or x = -89
- [| x |] = 89 then x is in the interval [89; 90)
- The limit of the sequence x n= 89 + 1 / n is 89 when n has infinity
- The limit of f (x) = 4x + 85 is 89 when x tends to 1
- The function | x-89 | / (x-89) has no limit when x tends to 89 [
