[ernestombayo7]

Originally Posted by Type R

Ernesto,

I quote your article: -

"Infinity cannot be found in the physical universe. The universe contains millions of galaxies, each containing millions of stars, each containing trillions of particles --- but only finitely many."

There is a problem with this statement. It is looking for infinites in discrete particles: atoms, nuclei, electrons, etc. It would seem wise to infer that such objects are finite in number, though extreme in number. I cannot refute this.

I agree.and all of science mathematics and philosophjy agrees.that actual infinites cannot exist.

But the title of this thread is "mathematicians..." Are mathematicians confined to studying elemental items? Don't mathematicians and scientists study motion, time, growth, etc? Doesn't motion exist? Don't events exist, even if only for the duration during which they occur?

As your article states, 'the abstract notion of "3" does not exist in the physical world -- it only exists in our minds'. So if you argue against infinity's existence, I will argue against zero, 3 and negative numbers -- and especially those horrible square roots of negative numbers (I will destroy complex maths, together with quantum physics and cars and aeroplanes and everything else that depends on mental fictions!) None of these things exist.

The correct statement would be,"none of this things physically exist."what the article means and am sure you know this is,we cannot find '1' or the number "2" floating inspace somewhere.it exists only in our minds.

but cars and aeroplanes physically exist.no matter what we try to map them to.they still physically exist.

Crudely put, the set "3" provides a 1-to-1 mapping between members of an abstraction called a set -- say {x, y, z} -- and physical reality: -

i agree.

When dealing with counting static distinct items in the physical, it is natural to look for distinct items like horses. But how about a non-static physical event (not item) like motion?

However, my earlier challenges regarding motion and time remain unmet: the number of points of time between 12:00 and 12:01 is infinite. A child on a swing goes through an infinite number of positions, yet the sum of infinity is finite! [The sum of some infinites is 1, the sum of other infinites is 2, the sum of other infinites is infinite].These are areas where breaking things into discrete items is wrong, but appropriate for our finite minds (like movie images).

You see even you analogy does not represent an actual infinite.it represents a potential infinite.the child on a swing does not undergo an infinite number of positions,that would suggest that its a complete set.
but as long as the child does not stop swinging it means new member/positions are being added.and thus still tending towards infinity.

Potential infinite:refers to a procedure that gets closer and closer to, but never quite reaches, an infinite end. For instance, the sequence of numbers 1,2,3,4,........

as long as new members can be added to the set.then its not an actual infinite. because an actual infinite:-

is an infinity that one actually reaches; the process is already done eg the set of all positive integers.it already has infinitely many members.

The challenges is to understand the nature of the different kinds of infinities (plural) and how they relate to one another, and if there is a separate mathematics for them.

As long as we can clearly see the difference between potential and actual infinite.then its pretty clear.

unless you throw in the complex theory of supertasks.

[Type R]

Furthermore, there are different kinds of infinity. Let's discuss only 1-dimensional types: -

#1, unbound infinity. e.g. all numbers.

#2, semi-bound infinity. e.g. all positive integers. Can go upwards forever, but has a lower limit.

#3, fully bound infinity. e.g. all fractions greater than 0 but less than 1. These are countless in number, but 0 and 1 are missing. To confuse Ernesto more, let's call these (as well as #2) non-infinite infinites...

You misunderstood the child on a swing sample. When the child makes one pendulum swing from back to front, say a 45 degree angle, every angle point in that 45 degrees (say, measured from the top backswing) has been covered (bound infinite), whether physically measurable or not. There are an infinite number of angles.

Your problem seems to relate to the difficulties of applying standard 1+1=2 maths to infinity. You haven't accepted that between two finite points, there can be an infinite number of points (I have, it occurred to me ages ago). You have a problem accepting that the sum total of an infinity can be 1. Or 2. You have a problem accepting that infinite set A can be a subset of infinite set B, yet be of the same infinite size at the same time.

These appear as disproofs to you, while to me they appear to be a new horizon of something fascinating and wonderful. I have always wondered whether there was a mathematics in which 1+1=1, or 1+1=0 ... and what it would mean?

Get over these hurdles, I advise. Think outside the box.