Yw. :cool:Thank you Proof! — punos
Yes (and as a conceptual analogue for Democritus-Epicurus' void), though I interpret the concept as temporal only and not, like Spinoza, also as eternal (i.e. unchanging, static).I'm curious to know if you agree with or subscribe to Spinoza's concept of natura naturans?
Yes (and as a conceptual analogue for Democritus-Epicurus' void), though I interpret the concept as temporal only and not, like Spinoza, also as eternal (i.e. unchanging, static). — 180 Proof
I have not found an officially recognized operator, mathematical or logical, that decomposes a 0 into -1 and +1. The normal way of using the logical NOT operator is (NOT 0 = 1, or NOT 1 = 0), but what I am saying is that there needs to be a version of the NOT operator that: (NOT 0 = -1, +1), (NOT -1 = no effect, NOT +1 = no effect).
You are probably familiar with functions that take the number line into itself. An example is $f(x)=1/x:$ it takes a number $x$ from the number line as input and returns $1/x$ as output. Unfortunately, the function is not defined at $x=0$ because division by $0$ is not allowed. However, as $x$ gets closer and closer to $0,$ $f(x)$ gets closer and closer to plus infinity if you're coming from the positive side, or minus infinity if you're coming from the negative side. If you could treat plus and minus infinity as one and the same ordinary point, then the function could be defined at $x=0$ and would be perfectly well behaved there. You can also define functions that take the plane into itself (the complex function $f(z)=1/z$ is an example) and again they may not be defined at every point because you have division by 0. However, by treating infinity as an extra point of the plane and looking at the whole thing as a sphere you may end up with a function that's perfectly tame and well behaved everywhere. A lot of complex analysis, the study of complex functions, is done on the Riemann sphere rather than the complex plane.
Anyhow, when we look at what happens when we approach 0/0 an interesting thing occurs. If we start with one as the numerator, and keep reducing the numerator towards zero, our number gets closer and closer to 0. On the flip side, when we keep reducing the denominator our result will tend towards the infinite. If you reduce both equally you get something like:
1/1 = 1
0.1/0.1 = 1
0.01/0.01 = 1
0.000....1 / 0.000...1 = 1 — Count Timothy von Icarus
A (maybe too simplistic) way to think of this might be "the amount of nothing is no space." No nothing is something, but it's a sheer nothing that, occupying no space, can't vary along any dimension, making it contentless. — Count Timothy von Icarus
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