 Originally Posted by nietstein
Well, you would have to know with absolute certainty what the future holds for it to be "bullshit" as you so have so eloquently labeled it. The concepts of zero and infinity are not so logically clearly cut and rational as you would like to believe they are. It sounds to me as though you would have happily claimed the earth was flat because other people said so. If there were not people willing to open their minds beyond the conventional logic of their time, where would we be today? Perhaps with an earth that is 'indubitably' flat and the center of the universe because others were fearful of the notion that it could be any other way.
Do you even read other people's posts before you write this rubbish? That was rhetorical; obviously you don't.
 Originally Posted by tempusername
Xei, if you retrace logical steps you've previously utilized it is obvious there is only one way for nietstein's claim to be true and that is if it is an axiom. You've mentioned before how
and even how the faculties by which we obtain truth (aka knowledge of axioms) are not a priori and completely wrong. So it seems instead that the bullshit is how you're actually in agreement with nietstein, in agreement over how infinity and 0 have potential to be one and the same thing.
But before I continue what do ℕ and ∅ represent? I only ever went up to Algebra III in an academic environment. Hng
Wow, I'm flattered you've being paying so much attention. But I don't really espouse the view that there is no such thing as truth. Truth comes in degrees of certainty, or ubiquity. Some truths come in degrees so high that it's insane not to believe them, and certainly insane to firmly believe otherwise. These truths are demonstrated via observations and inferences so pervasively ubiquitous that it makes no sense to dispute them.
At any rate, one thing I cannot permit is people using nonstandard language to make nonsense statements and pass them off as wisdom.
By definition, two sets have the same number of elements if you can construct a 'one-to-one' relationship from the elements of one to the elements of the other. For instance, if you have a set of five sheep, you can label the sheep one to five, and this defines a one-to-one mapping between the set of sheep and the set {1, 2, 3, 4, 5}. Or the set {2, 4, 6, 8, 10}; you can construct a map from this to {1, 2, 3, 4, 5} which sends each number to half of itself (and sending stuff in the other direction doubles it). The number 5 is literally defined as those sets which can be put into a one-to-one mapping with {1, 2, 3, 4, 5}. The number 0 is defined as those sets which can be put into a one-to-one mapping with {}, or '∅', the set of no elements, and the number 'infinity' is taken to mean those sets which can be put into a one-to-one mapping with {1, 2, 3, 4, ... }, or 'ℕ', the set of all positive whole numbers. The number of even numbers is thus infinity, for example, because again we can send 2 to its half, 1, 4 to 2, 6 to 3, and so on; this is a one-to-one map.
If you think about this for a bit, it's obvious that this formalism corresponds exactly to our common concepts of counting, 0, and infinity.
Is infinity equal to 0? Well, simply by the definition of the terms, this is equivalent to asking if we can send a one-to-one map from ℕ to ∅. Can we? No, obviously not. Because for a start we would need to map 1 (which is in ℕ) to something in ∅, yet there is nothing to map it to, because by definition ∅ is has no elements to be mapped to. Therefore infinity cannot be equal to 0.
It is anticipated that the OP will retort that this is not somehow what he meant. As the only thing that I have done is defined exactly what we commonly mean by the words he used, this will be an admission of the fact that his post was at best a failure of communication, at worst meaningless in the first place; in common parlance, 'bullshit'.
I've had one too many Tuborgs and this post may be overly long and rambling, sorry if that's the case.
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