The numberline shows us an order, and this order gives zero a place. But zero has no place within an order, because it would mean that there is a position of no order within that order, which is contradictory. — Metaphysician Undercover
I still don't see the confusion over negatives and their operations, but then I "do" math every day. Oftentimes familiarity makes it difficult to see how others must view the same. — Real Gone Cat
rotation — Pie
This is the very problem I referred to. The numberline shows us an order, and this order gives zero a place. But zero has no place within an order, because it would mean that there is a position of no order within that order, which is contradictory. Set theory suffers this problem which I discussed extensively with fishfry, who insisted that a set with no order is a coherent concept.
In common usage though, negative numbers are used to represent quantitative values, and here zero has a justified meaning. So it is the equivocation in usage, between "negative numbers" representing quantitative values, and "negative numbers" representing positions in an order, which causes a problem. — Metaphysician Undercover
So -4 = i×i×4i×i×4. A u-turn of whatever +4 is; — Agent Smith
It appears that our number system is as of yet still incomplete! — Agent Smith
but thought so because dividing by 0 gives infinity, and going smaller would have to mean going past infinity. Strange indeed. — Jerry
we stopped treating mathematics as uncovering truth about the world or as something real, and more as a formal set of rules that we stopped treating negatives as something spooky. — Jerry
Perhaps I didn't read far enough, but the person mentioned that believed negatives were greater than infinity was John Wallis, who actually did accept them, but thought so because dividing by 0 gives infinity, and going smaller would have to mean going past infinity. Strange indeed. — Jerry
It seems we accept negative numbers now on a similar footing as whole numbers, but complex numbers are still pretty hotly debated as to whether we should consider them as real as the real numbers. — Jerry
Most mathematicians seem to just take zero for granted, with zero understanding of what "zero" means. — Metaphysician Undercover
Most mathematicians seem to just take zero for granted, with zero understanding of what "zero" means. But of course, as I explained, the meaning of "0", as it is commonly used by mathematicians, is ambiguous — Metaphysician Undercover
But of course, as I explained, the meaning of "0", as it is commonly used by mathematicians, is ambiguous. — Metaphysician Undercover
Only in the sense that they have so many exact, formal systems that successfully employ zero that you'd want to know which successful specification of the concept was context relevant. — Pie
It is mind-blowing if you're into that stuff, but I'd say it's not at all surprising. — Metaphysician Undercover
↪jgill
It is mind-blowing if you're into that stuff, but I'd say it's not at all surprising — Metaphysician Undercover
There is no point at infinity in the complex plane. That point is by definition outside the plane. To allow it in is to break the rules of the structure. There is no north pole in the Reimann sphere — Metaphysician Undercover
This is why zero, like infinity, has no place within ordinal numbers, and must be excluded. — Metaphysician Undercover
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