I'm of the opinion an actual infinity cannot exist.
I would say that it simply isn't countable or computable. Yet it does in my view quite clearly define a quantity.1. A quantity is a specified amount of something. It has a limit. The infinite is that which has no limits and so cannot be quantified. Therefore, not a quantity as not quantifiable. — Mr Phil O'Sophy
Ammount of real numbers = infinite
Ammount of even real numbers = infinite
If different infinities have different values then is it really a definite quantity? — 3rdClassCitizen
Amount of real numbers = infinite
Amount of even real numbers = infinite
Does this mean that infinity divided by 2 equals itself?
Well, infinity is a very useful mathematical concept then. After all, the number "3" doesn't physically exist either.Infinity is a Mathematical fiction and should be applied carefully to the World of Physical Things. For example we can say that there are an Infinite number of Natural Numbers. Natural Numbers are Mathematical concepts. — SteveKlinko
Infinity is a Mathematical fiction and should be applied carefully to the World of Physical Things. For example we can say that there are an Infinite number of Natural Numbers. Natural Numbers are Mathematical concepts. — SteveKlinkoWell, infinity is a very useful mathematical concept then. After all, the number "3" doesn't physically exist either. — ssu
Space is definitely a Thing. There can be the 3D Space that we are familiar with, but there can also be 4D Space for example. 4D Space is a whole different Thing than 3D Space. If Space can be different Things then there can be no Space. That would be Absolute Nothingness.↪SteveKlinko I don't see how that's a given. Space is infinitely divisible. Whether or not space counts as a "thing" or not I don't think matters, but it's infinite. — MindForged
If space is a thing, it's not the same as the natural understanding of a thing. That's what I was talking about.
You're other point wasn't what I was talking about. I'm not saying space is infinite in breadth, but it can be infinitely divided without hitting some kind of base unit or boundary point. — MindForged
Actual Infinity is not a quantity:
- There is no number X such that X > all other numbers
- Because X+1 > X
Space is discrete that’s why we get paradoxes when we assume it’s continuous (Zeno’s paradoxes). — Devans99
The way you are solving the paradox uses the undefined quantity ‘infinity’ but I acknowledge there are other ways out of Zeno’s paradoxes other than discrete space.
Still I’d argue for discrete spacetime on the grounds:
- there is no such distance as 1/oo mathematically.
- Imagine a particle moving over a finite period of time. Continuous spacetime would require the particle to have occupied a actually infinite number of states which is nonsensical.
Still even if space is continuous, that would only be a potential infinity rather than actual infinity. — Devans99
If a particle only occupied discrete states then according to your theory it would have to jump from position to position while moving. It would necessarily have to stop at each position for the time it would take to continuously travel between two of the positions. — SteveKlinko
The Infinitely Large and the Infinitely Small are a real pain in the Brain.If a particle only occupied discrete states then according to your theory it would have to jump from position to position while moving. It would necessarily have to stop at each position for the time it would take to continuously travel between two of the positions. — SteveKlinko
A good point. It depends on your view of time as to whether you think the particle exists in an actually infinite number of states:
- Presentist. The past does not exist. So the particle does not exist in an Actually Infinite number of states, just one state, the present.
- Eternalist. The past exists so continuous time implies the particle must exist in an actually infinite number of states.
Presentism leads to paradoxes, so that suggests Eternalism. But time must be discrete for Eternalism to be free of Actual Infinity (which I class a paradox). — Devans99
But now imagine the Square growing to Infinite size. The sides would all move out to infinity. No matter how far you went in the universe you would never encounter a side of the Square. — SteveKlinko
Is infinity properly thought of as a number? Is it a quantity? Is that the same question — frank
Is infinity properly thought of as a number? Is it a quantity? Is that the same question? — frank
In the first case, infinity is a shorthand for a limiting process (the infinity is hidden in the quantifier 'for all epsilon') — fdrake
Nothing to prevent you from adding 1 to infinity. — tom
In the second case - for cardinals - they give the size of infinite sets, so yes they are probably quantities since they represent the magnitude of something. — fdrake
I don't think cardinality offer a quantitative view of Infinity, since it is either a relation between a set and its elements or between its elements and numbers(e.g. a set is D-
infinite iff for every natural number the set has a subset whose cardinality is that natural number) or between sets(e.g. the cardinal of R is bigger than the cardinal of I) — Ikolos
Numbers are sets, in the usual axiomatizations, so cardinality very naturally fits our idea of quantity. — SophistiCat
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