Ah, we finally get to the heart of the matter--it is not that the definition of infinity is contradictory, as the thread title asserts, but that you do not like including something in mathematics that does not follow the same rules as finite quantities — aletheist
Again to the op - infinity is not a number- it is a concept — Rank Amateur
Indeed, infinity is different from any finite quantity. So what? That does not make it illogical or contradictory, just different — aletheist
Why? The fact of the matter is that it does not, so we can either throw up our hands (like you do) or find and develop meaningful alternatives (like mathematicians have). — aletheist
How many numbers are there? How many square numbers are there? — aletheist
See, the only thing contradictory in this entire discussion is your childish insistence on repeatedly applying the axioms of finite mathematics to infinity. Your "induction" here is straightforwardly false. — aletheist
You have yet to identify a single contradiction when the relevant terms are defined consistently, and a paradox is simply an opportunity to think more carefully. — aletheist
What is not logical is the claim that "1+∞ = ∞ implies 1 = 0"; it reveals an utter lack of understanding about the mathematics of infinity, which at this point is clearly willful — aletheist
The author of the definition that you quoted would presumably reply: It is an infinite number. — aletheist
Once again, you are smuggling in an additional premise--in this case, that something must be assignable or countable in order to qualify as a number — aletheist
A triangle cannot be a number. Does that mean geometry is not mathematics? — aletheist
Read the definition that you quoted more carefully. It does not state, "A number greater than any number," which would indeed be contradictory. Instead, it states, "A number greater than any assignable quantity or countable number," which is not contradictory at all — aletheist
t's a defective definition, thus not good for anything including posts about it. — tim wood
Current science can't tell us about an alleged start to time. — S
people will readily admit that the real between 0 and 1 are infinite despite — MindForged
you even chose not to believe the mathematical definition of a point - because it didn't fit your position — Rank Amateur
Faith - can not be in conflict with fact or reason — Rank Amateur
I don't think it is intended to, and logic has nothing at all to do with it. At least in Catholicism - it is referred to as the mystery of the Trinity - it is outside reason, it is a matter of faith — Rank Amateur
"The number of events in an infinite regress is greater than any finite number," but that is not self-contradictory at all; in fact, it is trivially true. — aletheist
"A magician pulling a rabbit from a hat without using a trick of some sort.
— Devans99
That is actually impossible, but not logically impossible. — aletheist
Again, that is indeed actually impossible; but it is not logically impossible, because we can imagine it. — aletheist
I would say that that's optimistic. I seem to have thrown a spanner in the works. But I wish you the best of luck in that endeavour. It has certainly been interesting so far to examine what you've been coming up and to subject it to scrutiny. — S
Please give me an example of something that you can imagine, yet is logically (not just actually) impossible. — aletheist
Please tell me exactly how you can imagine squaring the circle. — aletheist
A real circle is truly continuous, and its mere possibility is sufficient for its reality. — aletheist
it logically follows that your model is impossible. — S
a point is a specific place in space, it has no size — Rank Amateur
And it would regress in that way infinitely. — S
just for some mathematical clarity - between any two points- whether it is on a circle or a line are an infinite number of points. — Rank Amateur
What we can draw on paper is a representation of a circle, and we can mark as many points on it as we like--up to any finite number. However, a real circle--note, not an actual circle, since there is no such thing--does not consist of any number of discrete points, finite or infinite; it is a continuous curve, infinitely divisible into smaller and smaller arcs — aletheist
hierarchy of infinities — MindForged
Aristotle believed actual infinities were impossible but they are not — MindForged