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<DIV>One digit numbers would normally be considered to have their digits in decreasing order. (They're also in increasing order.) Formally, the condition is: for all i,j, if i < j, then d(i) > d(j). For a one-digit number, the condition i < j is always false, so the implication is always true. Or to put it another way, where do they fail to descend?</DIV>
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<DIV>Franklin T. Adams-Watters<BR> <BR>-----Original Message-----<BR>From: zak seidov <zakseidov@yahoo.com><BR><TT>Neil, Eric, seqfans,<BR><BR> Neil gives in OEIS :<BR><BR>A009995 Digits in decreasing order. <BR> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 30, 31, 32,<BR>40, 41, 42, 43, 50, 51, 52, 53, 54,... <BR><BR> While Eric gives Rf. as follows:<BR>(Eric W. Weisstein. "Digit." From MathWorld--A Wolfram<BR>Web Resource. <BR><A href="http://mathworld.wolfram.com/Digit.html" target=_blank>http://mathworld.wolfram.com/Digit.html</A> )<BR>in his Table;<BR><BR>A009995 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50,<BR>51, ... <BR><BR>And Eric notes that numbers =>10.<BR><BR>It seems that one-digit numbers<BR>0, 1, 2, 3, 4, 5, 6, 7, 8, 9 <BR>should be omitted from A009995, <BR>right?<BR><BR>In which sense these one-digit numbers have <BR>"digits in decreasing order"? <BR><BR>BTW If we omit one-digit numbers<BR>then total number of decimal numbers with!
<BR>"digits in decreasing order"<BR>would be 1013, not 1023=2^10-1 <BR>as both Eric and Neil claim. <BR><BR>What I'm missing? <BR><BR>Zak<BR><BR>__________________________________________________<BR>Do You Yahoo!?<BR>Tired of spam? Yahoo! Mail has the best spam protection around <BR><A href="http://mail.yahoo.com" target=_blank>http://mail.yahoo.com</A> <BR></TT></DIV><!-- end of AOLMsgPart_0_7fb2dec0-6b15-4ec0-8404-dd7ae94e64a6 --></DIV></DIV>
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