Pushforward measure - Revision history

184.23.19.241 at 07:02, 30 July 2014

2014-07-30T07:02:02Z

← Older revision		Revision as of 09:02, 30 July 2014
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	~~{{Infobox number~~		The writer is called Araceli Gulledge. Interviewing is what she does but quickly she'll be on her own. What she enjoys doing is to play croquet but she hasn't produced a dime with it. Her family life in Idaho.<br><br>my page; [http://Royalcajun.com/UserProfile/tabid/57/userId/17325/Default.aspx http://Royalcajun.com]
	~~\| number = 495~~
	}}
	~~'''495'''~~ is ~~the integer after 494 and before [[496 (number)\|496]]~~. It is ~~a [[pentatope number]] (and so a [[binomial coefficient]] <math> \tbinom {12}4 </math>)~~.

	~~== Kaprekar transformation ==~~

	~~The Kaprekar transformation~~ is ~~defined as follows for three-digit numbers:~~
	~~# Start with~~ a ~~three-digit number~~ with ~~at least two digits different~~.
	~~# Arrange the digits in ascending and then~~ in ~~descending order to get two three-digit numbers, adding leading zeros if necessary~~.
	~~# Subtract the smaller number from the bigger number.~~
	~~# Go back to step 2.~~

	~~Repeating this process will always reach 495 in a few steps. Once 495 is reached, the process stops because 954 – 459 = 495.~~

	~~=== Example ===~~

	~~For example, choose 589:~~

	~~:985 − 589 = 396~~
	~~:963 − 369 = 594~~
	~~:954 − 459 = '''495'''~~

	~~The only three-digit numbers for which this function does not work are [~~[~~repdigit]]s such as 111, which give the answer [[0 (number)\|0]] after a single iteration. All other three-digits numbers work if leading zeros are used to keep the number of digits at 3~~:

	~~:211 – 112 = 099~~
	~~:990 – 099 = 891 (rather than 99 - 99 = 0)~~
	~~:981 – 189 = 792~~
	~~:972 – 279 = 693~~
	~~:963 – 369 = 594~~
	~~:954 − 459 = '''495'''~~

	~~The number [[6174 (number)\|6174]] has the same property for the four-digit numbers~~.

	~~==See also==~~
	*[[Collatz conjecture]] — sequence of unarranged-digit numbers always ends with the number 1.

	~~==References==~~
	*{{cite journal\|last=Eldridge\|first=Klaus E. \|coauthors= Sagong, Seok\|title=The Determination of Kaprekar Convergence and Loop Convergence of All Three-Digit Numbers \|journal= The American Mathematical Monthly\|volume=95\|issue=2\|date=February 1988\|pages=105–112\|doi=10.2307/~~2323062\|publisher=The American Mathematical Monthly, Vol. 95, No~~. ~~2\|jstor=2323062}}~~

	~~[[Category:Integers\|49e02 495]]~~

	~~[[fr:Nombres 400 à 499#495]]~~
	~~[[ja:400#481 から 499]~~]

en>Yobot: Reference before punctuation detected and fixed using AWB (9585)

2013-11-07T22:03:14Z

Reference before punctuation detected and fixed using AWB (9585)

← Older revision		Revision as of 00:03, 8 November 2013
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	~~Friends contact him Royal Seyler~~. ~~Interviewing~~ is ~~what she does but quickly she'll be on her own. Years ago we moved to Kansas~~. The ~~preferred hobby~~ for ~~him~~ and ~~his kids is~~ to ~~generate and now he~~ is ~~trying to make money with it~~.~~<br><br>my web page~~ :: [~~http~~:~~//Changbai~~.~~Newdrycleaning~~.~~com~~/~~photo/54180 Changbai~~.~~Newdrycleaning~~.~~com~~]		{{Infobox number
			\| number = 495
			}}
			'''495''' is the integer after 494 and before [[496 (number)\|496]]. It is a [[pentatope number]] (and so a [[binomial coefficient]] <math> \tbinom {12}4 </math>).

			== Kaprekar transformation ==

			The Kaprekar transformation is defined as follows for three-digit numbers:
			# Start with a three-digit number with at least two digits different.
			# Arrange the digits in ascending and then in descending order to get two three-digit numbers, adding leading zeros if necessary.
			# Subtract the smaller number from the bigger number.
			# Go back to step 2.

			Repeating this process will always reach 495 in a few steps. Once 495 is reached, the process stops because 954 – 459 = 495.

			=== Example ===

			For example, choose 589:

			:985 − 589 = 396
			:963 − 369 = 594
			:954 − 459 = '''495'''

			The only three-digit numbers for which this function does not work are [[repdigit]]s such as 111, which give the answer [[0 (number)\|0]] after a single iteration. All other three-digits numbers work if leading zeros are used to keep the number of digits at 3:

			:211 – 112 = 099
			:990 – 099 = 891 (rather than 99 - 99 = 0)
			:981 – 189 = 792
			:972 – 279 = 693
			:963 – 369 = 594
			:954 − 459 = '''495'''

			The number [[6174 (number)\|6174]] has the same property for the four-digit numbers.

			==See also==
			*[[Collatz conjecture]] — sequence of unarranged-digit numbers always ends with the number 1.

			==References==
			*{{cite journal\|last=Eldridge\|first=Klaus E. \|coauthors= Sagong, Seok\|title=The Determination of Kaprekar Convergence and Loop Convergence of All Three-Digit Numbers \|journal= The American Mathematical Monthly\|volume=95\|issue=2\|date=February 1988\|pages=105–112\|doi=10.2307/2323062\|publisher=The American Mathematical Monthly, Vol. 95, No. 2\|jstor=2323062}}

			[[Category:Integers\|49e02 495]]

			[[fr:Nombres 400 à 499#495]]
			[[ja:400#481 から 499]]

en>DannyAsher: /* Main property: Change of variables formula */

2012-08-12T15:16:21Z

Main property: Change of variables formula

New page

Friends contact him Royal Seyler. Interviewing is what she does but quickly she'll be on her own. Years ago we moved to Kansas. The preferred hobby for him and his kids is to generate and now he is trying to make money with it.<br><br>my web page :: [http://Changbai.Newdrycleaning.com/photo/54180 Changbai.Newdrycleaning.com]