hi, i am posting the mathematical identities i wrote last year because they are orientated around sequences and series, binary sequences, thus may serve useful for those who employ digital logic in C programming due to its modular nature when employed in ino sketches.(infinitely looped as "default")
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B(i,j) examples using the piece wise form for the Kronecker delta in place of the trig identity form defined above, so that you can see the base = 10 in the series more clearly.
sorry if it doesnt say somewhere, the upper cornered brackets is the ceiling of the arg and lower cornered brackets for floor of arg. curly brackets are the fractional part( or x-floor(x))
rephrased.
if(x1=a0&&x1=!a1&&x1=!a2...&&x1=!aN){some arbitrary digital I/O commands} is equivalent to specifying a particular output configuration IF AND ONLY IF an individual input 'x1' state is a0 value a finite set of N distinct possible states, {a0,a1,a2,...aN}. conversely, you can define the output state of "N' digital output pins of one MCU to supply an exclusive input configuration in another MCU.
i used it to generate the prime number subset, because the maple kernel was crashing when i tried generating the primes using the Kronecker delta in its usual piece wise form. when i used the trig identify it produces the subset smoothly.
I said POSSIBLY useful. imagination maybe required.
think of something like if(x1=x0&&x1=!x2&&x1=!x3...&&x1=!xN) ...
I'm thinking of something like, "Why would anyone write a pointless statement like that and what does it have to do with Kronecker's delta function?"
... is equivalent to specifying an individual element's value a finite set of N distinct objects
which makes no sense.
I think this is another of your "epic brain fail[s]".
Pete
the function B(i,j) is a mapping of a number's decimal digits to an integer sequence on an acending index n =1,2,3 so things that come to mind, encoding data based on being able to obtain its digital root via this method (the number 225 has a digital root 2+2+5)
I don't see how B(i,j) does what you claim. Give us a detailed, worked out, example of how the B(i,j) "function" maps the number 25 into its so-called "digital root". Where did you get this "function" from anyway?
Pete
i wrote it last year as a result of having CPU processing not handling generating prime number sets when expressed in piece wise brackets. what do you mean you dont see how it does what i claim i even put up the maple extract for you. if its not working it will have something to do with whatever mathematics software you are using not having had a "package" loaded on your worksheet which is basically those programs equivalent to an ino's libraries that you have installed.
image files read the image files.
as the numbers got larger, the computer struggled more with using the piece wise for as in the example of a = 345 i used in the maple extract. so that was hence what lead to me looking for something like that trig identity to express the Kronecker delta in a sequence
the digital root is the summation of the terms in the sequence generated when evaluating B
If your B(i,j) function actually had a real purpose and you actually understood it, it would be trivial for you to explain how it works for a number as small as 25. Instead you generate more rubbish - and for the record, I have looked at all your images, which is why I asked the question.
I am utterly unimpressed by your ability to string together mathematical symbols into a sequence of nonsensical "equations" which you then "explain" by spewing bafflegab that is largely devoid of any punctuation.
Pete
do you have maple? or an equivalent i can try an convert it to for you? dont mess yourself about it chief.
everything is trivial to an extent of course its as trivial as any equality relation is.
the decimal system is modular. trigonometric sequences and series are also modular -- periodic. it has as much purpose as anything really.