Devine Lu Ator
An interesting aspect of fractions and prime factorization is that multiplying fractions is the same as adding the prime numerators and subtracting the prime denominators.
For example, multiplying 42 by 5/14 means incrementing the power of prime 5, and decrementing the power of primes 2 and 7 — For a result of 42. A division is simply the inversion of the effects of the numerator and denumerator.
⛧ numerik ⛧
@neauoire @alderwick correct. if i give you X and say that i just multiplied some number by 1 you know that the number was X.
if i give you 0 and say that i just multiplied some number by 0 you can't possibly know which one i used.
Devine Lu Ator
@d6 @alderwick so zero can't exist at all in a reversible framework where you go back and forth with multiplications and divisions
⛧ numerik ⛧
@neauoire @alderwick annihilation isn't a gate (or a mirror) in this interpretation. you are throwing away the information contained in the other argument. it doesn't depend on the input at all.
Devine Lu Ator
@d6 @alderwick is it tho? For one input bit, there are two possible reversible gates. One of them is NOT. The other is the identity gate, which maps its input to the output unchanged.
If annihilation is the mirror to identity, shouldn't it be reversible?
⛧ numerik ⛧
@neauoire @alderwick for addition, zero is the identity element (x + 0 = 0 + x = x).
for multiplication, one is the identity element (x * 1 = 1 * x = x). zero is called the annihilator (x * 0 = 0 * x = 0). addition does not have an annihilator.
⛧ numerik ⛧
@neauoire @alderwick no, there's no exponent that you can raise a prime number to which gives you zero.
2^0 * 3^0 * ... = 1.
you can only reach zero using zero and once you're there you can never leave.
Devine Lu Ator
@alderwick can zero be presented in the format in the picture above? Like, does zero exist in the prime factorization layout? If a multiplication by 0 is equal to setting all prime factors to zero, zero has in a sense awareness of what is being multiplied by it, does it not?
Andy Alderwick
@neauoire Yep!
Devine Lu Ator
@alderwick mul by zero and div by zero are both equally unreversible right?
Andy Alderwick
@neauoire (referring to your earlier toot about dividing by zero) This is why zero is bad and should be avoided. You can multiply by any other number and you can go back by dividing by the same number. But not with zero: ban zero now! As you can see, I have an infinitesimal-tolerance policy.
Devine Lu Ator
@d6 @alderwick just looked it up, and all the results about this are on quantum computing in regards to entropy loss *swimgs back to the shallow end of the pool*
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