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|---|---|---|---|---|
| Cardinal | one hundred seventy | |||
| Ordinal | 170th (one hundred seventieth) | |||
| Factorization | 2 × 5 × 17 | |||
| Divisors | 1, 2, 5, 10, 17, 34, 85, 170 | |||
| Greek numeral | ΡΟ´ | |||
| Roman numeral | CLXX | |||
| Binary | 101010102 | |||
| Ternary | 200223 | |||
| Senary | 4426 | |||
| Octal | 2528 | |||
| Duodecimal | 12212 | |||
| Hexadecimal | AA16 | |||
170 (one hundred [and] seventy) is the natural number following 169 and preceding 171.
170 is the smallest n for which φ(n) and σ(n) are both square (64 and 324 respectively). But 170 is never a solution for φ(x), making it a nontotient. Nor is it ever a solution to x - φ(x), making it a noncototient.
170 is a repdigit in base 4 (2222) and base 16 (AA), as well as in bases 33, 84, and 169. It is also a sphenic number.
170 is the largest integer for which its factorial can be stored in IEEE 754 double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10306.[ citation needed ]
There are 170 different cyclic Gilbreath permutations on 12 elements, [1] and therefore there are 170 different real periodic points of order 12 on the Mandelbrot set. [2]
In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.
In mathematics, the Fibonacci sequence is a sequence in which each term is the sum of the two terms that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some from 1 and 2. Starting from 0 and 1, the sequence begins
The Mandelbrot set is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not diverge to infinity when iterated starting at , i.e., for which the sequence , , etc., remains bounded in absolute value.
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work.
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
222 is the natural number following 221 and preceding 223.
23 (twenty-three) is the natural number following 22 and preceding 24.
51 (fifty-one) is the natural number following 50 and preceding 52.
58 (fifty-eight) is the natural number following 57 and preceding 59.
93 (ninety-three) is the natural number following 92 and preceding 94.
114 is the natural number following 113 and preceding 115.
In mathematics, and more particularly in number theory, primorial, denoted by "pn#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers.
720 is the natural number following 719 and preceding 721.
116 is the natural number following 115 and preceding 117.
118 is the natural number following 117 and preceding 119.
225 is the natural number following 224 and preceding 226.
168 is the natural number following 167 and preceding 169.
288 is the natural number following 287 and preceding 289. Because 288 = 2 · 12 · 12, it may also be called "two gross" or "two dozen dozen".
In number theory, the Kempner function is defined for a given positive integer to be the smallest number such that divides the factorial . For example, the number does not divide , , or , but does divide ,so .
A Gilbreath shuffle is a way to shuffle a deck of cards, named after mathematician Norman Gilbreath. Gilbreath's principle describes the properties of a deck that are preserved by this type of shuffle, and a Gilbreath permutation is a permutation that can be formed by a Gilbreath shuffle.
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