On 10/11/20 5:47 PM, Wes Turner wrote:
Indeed, perhaps virtual particles can never divide by zero and thus the observed laws of thermodynamic systems are preserved.
Would you please be so kind as to respond in the main thread so that this is one consecutive thread?
No, 2 times something is greater than something. Something over something is 1. If we change the division axiom to be piecewise with an exception only for infinity, we could claim that any problem involving division of a symbol is unsolvable because the symbol could be infinity. This is incorrect: x / 2 is unsolvable because x could be infinity x / 2 > x / 3 (where x > 0; Z+) is indeterminate because if x is infinity, then they are equal.
Which of these are you arguing should fail if Python changes to returning [+/-]inf instead of raising ZeroDivisionError?
assert 1 / 0 != 2 / 0 assert 2*inf > inf assert inf / inf == 1
All of them will fail. n / 0 is inf or -inf depending on whether n is positive or negative (and I believe 0/0 is NaN)
n * inf is inf, for all n > 0
inf / inf in NaN (if I remember right).
infinity is NOT just a number that behaves like any finite number.
Maybe you should look into the rules for transfinite mathematics, a lot of the rules that apply for finite mathematics don't work when you allow for non-finite numbers.
Note, that for example you last example, the answer of Z+ is correct, as Z+ does NOT include infinity, so the case where x is infinity, is outside the domain Z, or even R.
Also note, the the Axioms like the Division Axiom apply to the domains of Finite numbers, and not all of them apply when you get Infinities. This is just like some properties in the Real do not apply when you move to the Complex plane.
On Sun, Oct 11, 2020 at 5:41 PM Richard Damon <Richard@damon-family.org mailto:Richard@damon-family.org> wrote:
On 10/11/20 5:04 PM, Wes Turner wrote: > So you're arguing that the scalar is irrelevant? > That `2*inf == inf`? > > I disagree because: > ```2*inf > inf``` > > And: > > ```# Given that: > inf / inf = 1 > > # When we solve for symbol x: > 2*inf*x = inf > 2*x = 1 > x = 1/2 > > # If we discard the scalar instead: > 2*inf*x = inf > inf*x = inf > x = 1 > > # I think it's specious to argue that there are infinity solutions; > that axioms of symbolic mathematics do not apply because infinity > ``` > Treating inf as any other number because it works out 'symbolically' is one of the recipes that allow you to prove that 1 == 2, thus symbolic math needs to work with certain preconditions that avoid the generation of 'numbers' like infinity into the system (or somewhat related, avoid a divide by 0) -- Richard Damon _______________________________________________ Python-ideas mailing list -- firstname.lastname@example.org <mailto:email@example.com> To unsubscribe send an email to firstname.lastname@example.org <mailto:email@example.com> https://mail.python.org/mailman3/lists/python-ideas.python.org/ <https://mail.python.org/mailman3/lists/python-ideas.python.org/> Message archived at https://firstname.lastname@example.org/message/SQNY5WFVPRPWXRZ7FW3H3RUGM3UCLCCL/ <https://email@example.com/message/SQNY5WFVPRPWXRZ7FW3H3RUGM3UCLCCL/> Code of Conduct: http://python.org/psf/codeofconduct/ <http://python.org/psf/codeofconduct/>
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