Quote Originally Posted by Xei View Post
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.
I find it inconceivable that truths come in degrees of certainty. The relativity of so many things within the universe surely constitutes the ubiquity of particular truths, especially when it comes to Earthly or human things. Though I can't correlate relativity to degrees of certainty. Certainty is more so a property of human understanding than truth, no? People can have different levels of clarity/certainty/understanding about a truth but that doesn't effect the tangibility of the truth.

this post may be overly long and rambling, sorry if that's the case.
It isn't. And now that I've relearned this bit about functions thanks to you I might actually be able to back up nietstein's claim. Though I am sort of hesitant to defend it after seeing you retort basically as Xei expected, nietstein ;\

But hey

All I can think about is Russel's Paradox. In defining ∅ as a set with no elements do we not instantaneously ascribe that the set cannot be an element--that it cannot be a member of itself? By distinguishing ∅ at all, do we not create a Russel set? ∅ cannot be a member of itself because it has no elements, yet in satisfying that definition of itself, it inevitably and contradictorily becomes a member of itself, an element, a 1.

So
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.
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