When we subtract some number m from another number n, we are essentially creating a relationship between n and m such that whatever the difference is, can be treated as a 'local identity' (relative value of '1') for n, and the base then becomes '(base n/(n-m))%1' (the floating point component).

for example, take any number, say 512

here, 697 is a partial multiple of our new value of '1' whose actual value is the difference (697-512) 185 in base 10. proper multiples on this example number line, based on natural numbers, would be
185*3, etc

The translation factor between these number lines becomes


multiplying any base 10 number by this, puts it on the 1:185 integer line.

Once on a number line other than 1:10, you must multiply by the multiplicative identity of the new number line (185 in the case of 1:185), to get integers on the 1:10 integer line back out.

185*0.7675675675675677 for example gives us


This value, pulled from our example, would be 'zero' on the line.

185 becomes the 'multiplicative' identity of the 1:185 line. And 142 becomes the additive identity.

Incidentally the proof of this is trivial to see just by example. if 185 is the multiplicative identity of 697-512, and and 142 is the additive identity of number line 1:185

then any number '1', or k=some integer, (185*(k+0.7675675675675677))%185
should equal 142.

because on the 1:10 number line, any number n%1 == 0

We can start to think of the difference of any two integers n, as the multiplicative identity of a new number line, and the floating point component of quotient of any number n to the difference of any number n-m, as the additive identity.

let n =697
let m = 185
n-m == '1' (for the 1:185 line)

(n-m) * ((n/(n-m))%1) == '0'

As we can see just like on the integer number line, n%1 == 0
or in the case of 1:185, it equals 142, our additive identity.

And now, the purpose of this long convoluted post: all so I could bait people into reading a rant on division by zero.

  • 4
    I stopped at the second paragraph. Is this some kind of premature end of consumption?
  • 4
    You failed at your purpose. I skipped right to the end to see what you were on about, after reading like 2 sentences.
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    You should be whipped
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    @ostream that's wrong
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    @ostream won't spend energy on this. It's ridiculous
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    @retoor lol, it shows it isn't 34
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    @Demolishun it's also not something else
  • 1
    @Demolishun I researched poker and that taught me not to believe in such crap
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    @retoor I definitely deserve it.
  • 1
    @Wisecrack tell dem the truth about dices and average! No such thing
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    @ostream maybe you saw the same video that I saw about d20 on youtube. In that video it was about the d&d advantage roll where you take the higher number of two d20 rolls.
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    @Wisecrack Trying to completely understand ...
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    It all sounds like some bullshit and I'm not even sure it will correctly compute
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    @iiii maybe some people might be confused because python uses percentage sign as a substitute for the 'mod' keyword.

    If you work through the example careful enough, it starts to make sense.

    Obviously some things break like his subtracting zero (the additive identity) from one (the multiplicative identity), leaves 1 unchanged, whereas subtracting our '0', 142, from our '1', or 185, on the 1:85 number line, does not preserve the property of the multiplicative identity on this given number line (in the absolute sense).
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    @Wisecrack all of this does not make a group. That's it
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    @kobenz big D energy
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    @Wisecrack You're saying that 185 in base 10 is the multiplicative identity, i.e "1" in base 0.76756756756756 ?
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    @ViRaS It's not really 'base 10' in the sense of counting in some base. I don't really have the mathematical background (at all) to know what its called, I just used that word.
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    @kobenz Alright, now you're fucking with us.

    Doctor, have I gone crazy or not?
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    @iiii "all of this does not make a group. That's it"

    lol, I don't even know what a group is.

    But I'll find a way to handwave it and claim you're wrong just for funsies.
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    @iiii oh im just playing my guy.
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    @Wisecrack wtf? how can you know so much about maths and not know what a group is? 😄
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    @Lensflare high school in the inner city post 2000s didnt teach much.

    any resources you'd recommend on groups for beginners? Anything starting from first principles would be great.

    Also looking at the definition of groups, am I mistaken in assuming the math in the original post doesnt conform to the assocoativity necessary? I may be getting the terminology wrong but I hope the questions clear enough.
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    @Wisecrack I don’t know much about groups either. I just heard about them in some math videos on youtube like Numberphile.
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    @Wisecrack you're trying to map a multiplicative and additive group of real numbers onto not an additive group while claiming it having a property of an additive group (zero)

    Also, multiplying something by N and then taking a modulo N makes literally no sense to do. Just take a modulo without multiplying. And also taking an modulo of a non integer number is also quite a pointless operation
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    @iiii it obviously does make all the sense in the world! Here let me overcommitted to my error!
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