Again to the op - infinity is not a number- it is a concept — Rank Amateur
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
Because most people only ever deal with and think about finite quantities, which is the domain in which that axiom applies.The problem is infinity does not follow the axiom: 'if I add (non-zero) to something, it changes'. Thats such as basic axiom, taken as reality by most people... — Devans99
Because most people only ever deal with and think about finite quantities, which is the domain in which that axiom applies. — aletheist
The problem is that relativity does not follow the axiom: "no matter how fast something is traveling, mass, length, and time are constant." That is such a basic axiom, taken as a reality by most people ...The problem is infinity does not follow the axiom: 'if I add (non-zero) to something, it changes'. Thats such as basic axiom, taken as reality by most people... — Devans99
Infinity is not a number of any kind it is a label for a concept. — Rank Amateur
The problem is that relativity does not follow the axiom: "no matter how fast something is traveling, mass, length, and time are constant." That is such a basic axiom, taken as a reality by most people ... — aletheist
The problem is infinity does not follow the axiom: 'if I add (non-zero) to something, it changes'. — Devans99
But we have good evidence that the speed of light is constant and the rest follows. We have no evidence for 'stuff that we change that does not change' and it makes no logical sense anyway. — Devans99
It does change. The set has an element it did not have before. But the cardinality does not change. — MindForged
OK so thats equivalent to saying 'I have this set to which I can add to and the size does not change'. Thats nonsense - anything you add (non-zero) to the size changes. That should be an indisputable axiom of mathematics or at least derivable from simpler axioms. — Devans99
Indeed you are! Nothing wrong with opinions in their proper place and time. Nor pigs nor parlors, but there is with pigs in parlors. Your opinion is a pig that has slipped its pen and is playing in the parlor.I am entitled to my opinions. — Devans99
So that is:
- It's a number
AND
- It's greater than any number
The two are contradictory.
— Devans99
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.
Infinity can’t be a number. So it is not maths.
— Devans99
A triangle cannot be a number. Does that mean geometry is not mathematics? — aletheist
'when you change something, it is changed'. — Devans99
If only./thread — S
and already explain how this is false. The axiom that you are really following is, "When you add a finite quantity to another finite quantity, you get a different finite quantity." That axiom straightforwardly does not apply to infinity, which does not entail that infinity is somehow contradictory--only that it is different from a finite quantity, and must accordingly be treated differently than a finite quantity.'when you change something, it is changed'.
Infinity in mathematics does not follow this axiom. — Devans99
'when you change something, it is changed'
Do you buy it or not? If you buy it, you don't buy infinity. — Devans99
And that first bullet there is indeed an outdated tradition. Fortunately we know more these days. Cantor showed that there are infinite different infinites, no less; in a concise context, ∞ is ambiguous.Prior to Cantor's time, ∞ was
• mainly a metaphor used by theologians
• not a precisely understood mathematical concept
• a source of paradoxes, disagreement, and confusion — Eric Schechter
a set is infinite if and only if there is a bijection between the set and a proper subset of itself — jorndoe
Colloquially, ∞ could be thought of as a quantity that's not a (real) number. — jorndoe
I do not agree with the bijection procedure; it gives the wrong results; see Galileo's paradox. — Devans99
Galileo concluded that the ideas of less, equal, and greater apply to (what we would now call) finite sets, but not to infinite sets. In the nineteenth century Cantor found a framework in which this restriction is not necessary; it is possible to define comparisons amongst infinite sets in a meaningful way (by which definition the two sets, integers and squares, have "the same size"), and that by this definition some infinite sets are strictly larger than others. — https://en.wikipedia.org/wiki/Galileo%27s_paradox
No, it can't be thought of as a quantity; its defined as greater than any quantity therefore its is not a quantity. — Devans99
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