తొమ్మిది
తొమ్మిది (9) ఒక సహజ సంఖ్య, దీనికి ముందు గల సంఖ్య ఎనిమిది (8), మరియు తరువాత వచ్చే సంఖ్య పది (10).
వాడుకలో తొమ్మిదవ, తొమ్మిదో అనే పదాలను ఉపయోగిస్తారు. కొన్ని చోట్ల తొమ్మిదికి బదులు నవ ఉపయోగిస్తారు. ఉదాహరణకు తొమ్మిది గ్రహాలను నవగ్రహాలు అంటారు.తొమ్మిది ఒక మిశ్రమ సంఖ్య, దీని సరైన విభాజకములు 1 మరియు 3. ఇది 3 సార్లు 3 మరియు అలాగే 3 యొక్క స్క్వేర్ నంబర్. తొమ్మిది ఒక Motzkin సంఖ్య. ఇది మొదటి మిశ్రమ అదృష్ట సంఖ్య, దానితో పాటు మొదటి మిశ్రమ బేసి సంఖ్య. దశాంశ వ్యవస్థలో తొమ్మిది అత్యధిక సింగిల్ డిజిట్ నెంబర్. It is the second non-unitary square prime of the form (p) and the first that is odd. All subsequent squares of this form are odd. It has a unique aliquot sum 4 which is itself a square prime. Nine is; and can be, the only square prime with an aliquot sum of the same form. The aliquot sequence of nine has 5 members (9,4,3,1,0) this number being the second composite member of the 3-aliquot tree. It is the aliquot sum of only one number the discrete semiprime 15.
There are nine Heegner numbers.
Since 9 = 3, 9 is an exponential factorial.
8 and 9 form a Ruth-Aaron pair under the second definition that counts repeated prime factors as often as they occur.
In bases 12, 18 and 24, nine is a 1-automorphic number and in base 6 a 2-automorphic number (displayed as '13').
A polygon with nine sides is called a nonagon or enneagon. A group of nine of anything is called an ennead.
In base 10 a positive number is divisible by nine if and only if its digital root is 9. That is, if you multiply nine by any natural number, and repeatedly add the digits of the answer until it is just one digit, you will end up with nine:తొమ్మిది యొక్క గుణింతాలకు సంబంధించిన ఆసక్తికరమైన ఇతర నమూనాలు:
This works for all the multiples of 9.
"n" = 3 is the only other "n" > 1 such that a number is divisible by "n" if and only if its digital root is "n". In base N, the divisors of N − 1 have this property. Another consequence of 9 being 10 − 1, is that it is also a Kaprekar number.
The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. Examples:
Subtracting two base-10 positive integers that are transpositions of each other yields a number that is a whole multiple of nine. Examples:
This works regardless of the number of digits that are transposed. For example, the largest transposition of 35967930 is 99765330 (all digits in descending order) and its smallest transposition is 03356799 (all digits in ascending order); subtracting pairs of these numbers produces:
Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers, known as long ago as the 12th Century.
Every prime in a Cunningham chain of the first kind with a length of 4 or greater is congruent to 9 mod 10 (the only exception being the chain 2, 5, 11, 23, 47).
Six recurring nines appear in the decimal places 762 through 767 of pi. This is known as the Feynman point.
If an odd perfect number is of the form 36"k" + 9, it has at least nine distinct prime factors.
If you divide a number by the amount of 9s corresponding to its number of digits, the number is turned into a repeating decimal. (e.g. 274/999 = 0.274274274274...)
Nine is the binary complement of number six:
In probability, the nine is a logarithmic measure of probability of an event, defined as the negative of the base-10 logarithm of the probability of the event's complement.
For example, an event that is 99% likely to occur has an unlikelihood of 1% or 0.01, which amounts to −log 0.01 = 2 nines of probability.
Zero probability gives zero nines (−log 1 = 0). A 100% probability is considered to be impossible in most circumstances: that results in infinite improbability. The effectivity of processes and the availability of systems can be expressed (as a rule of thumb, not explicitly) as a series of "nines". For example, "five nines" (99.999%) availability implies a total downtime of no more than five minutes per year - typically a very high degree of reliability; but never 100%.
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