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.
assert 1 / 0 != 2 / 0
assert 2*inf > inf
assert inf / inf == 1
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```
> ```# 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)
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