Number 9

[Turtle]

Sure, toydel always does it. We ain't even from new yoyk either. Anyway osama ain't the only son of, and it ain't necessarily of a gun... it's the same for ben gurion anyway.

 

Yes, but suppose the starting number is single digit. It is equal to the sum of its digits so, when you subtract this from the starting number you get 0 and when you sum its digits you have 0.

So he's a bin gun after all, he looses the bet cuz he said it would be 9, even starting with a single digit number.

:doh:

 

mmmm...i may not understand the quibble still. :doh: but, if i may, i drew up a simple number line to illustrate my perspective. the top row are the integers, the bottom row have the values (underlined to distinguish them as range elements) of the digital root of the integer above. note the only "lone" zero is the integer zero, and the bottom line has no zeros at all. you can establish that 0 has a digital root of 9 by doing subtractions on the positive side away from the origin, such as 15/6-9/9=6/6. so we see subtracting a 9 from a 6 gives a 6. now move to the integer 6 on the number line and go left(subtract) 9 units to arive at -3, which we know has to have a digital root of 6. a few more such subtractions fills in the digital root pattern & showing 0 has a digital root of 9. notice only negative values with digital roots of 9 can actually have the digits added to get the root. in no case is there a digital root of 0. not sure if that's the parlor trick, but i grant it is somewhat tricky.

[Qfwfq]

note the only "lone" zero is the integer zero, and the bottom line has no zeros at all. you can establish that 0 has a digital root of 9 by doing subtractions on the positive side away from the origin, such as 15/6-9/9=6/6. so we see subtracting a 9 from a 6 gives a 6. now move to the integer 6 on the number line and go left(subtract) 9 units to arive at -3, which we know has to have a digital root of 6. a few more such subtractions fills in the digital root pattern & showing 0 has a digital root of 9.

Actually it makes sense to decree that 9 has a digital root of 0; whichever choice you make it is the additive neutral of the construct, so mathematicians prefer to use a 0-like symbol for it. That's why they call it "casting out the nines".

[Turtle]

Actually it makes sense to decree that 9 has a digital root of 0; whichever choice you make it is the additive neutral of the construct, so mathematicians prefer to use a 0-like symbol for it. That's why they call it "casting out the nines".

 

i agree that as long as we know they are interchangeable, & why, we can use whichever we like. i got in the habit of actually writing terms in different bases, so i'm comfortable with no zeros. doing it that way is fine at the start but quickly gets unworkable by reason of the multitude of unit symbols required. but, by the same token using the mod function starts returning multi-digit results just as hard to keep in mind. six of one, half a dozen of the other i suppose. :D

 

[Turtle]

Actually it makes sense to decree that 9 has a digital root of 0; whichever choice you make it is the additive neutral of the construct, so mathematicians prefer to use a 0-like symbol for it. That's why they call it "casting out the nines".

 

dear q, p, & other dear tender readers, no commentary on all this is complete without introducing buckminster fuller's take. :omg: it predates even me & u q. :hihi: (the last 2 pages of the synergetics thread, i screw down the vice vise on bucky's "9's": > synergetics)

 

going right to the old dead horse's mouth though...

synergetics:1200

1222.30 Casting Out Nines: We can use any congruence we like, and the pattern will be the same. The wave phenomenon, increasing by four and decreasing by four, is an octave beginning and ending at zero. From this I saw that nine is zero.

 

well, we agree with that...sort of. i mean he manages to see 9 is 0 & precedes the observation with this clarifying statement set:

1222.20 Cosmically Absolute Numbers: There are apparently no cosmically absolute numbers other than 1, 2, 3, and 4. This primitive fourness identifies exactly with one quantum of energy and with the fourness of the tetrahedron's primitive structuring as constituting the "prime structural system of Universe," i.e., as the minimum omnitriangulated differentiator of Universe into insideness and outsideness, which alone, of all macro-micro Universe differentiators, pulsates inside-outingly and vice verse as instigated by only one force vector impinging upon it. (See Sec. 624.)

 

well, gotta go sync my structure pulsations inside-outingly... . . .:ud:

[Proudclod229]

since our system of cells is composed of repeating parts, it should come as no surprise that composites of those parts produce other different repeating parts. i could as easily color up cells in "L's" -as in how a knight moves on a chess board- and get repeating patterns. while it's interesting visually, does it tell us anything mathematically about the system?

The reason that it is so interesting IS visual...you'll see.