Sarkus;

Trying to get through to you certainly feels like it.But so what if there is nothing "infinite" in the human experience? Seriously. So what?Maths isn't about human experience. It isn't even necessarily about reality. It is an abstraction. It is filled with concepts that have no "reality" but are meaningful tools.

How can you describe something you haven't experienced, like an alien abduction?

Measurement was a necessary practice in early history. Tracking time, recording inventory, business transactions, building structures, etc. That is human experience.

Math as a language was developed over centuries of experience. Today it is the verification tool for science.

Yes, there is such a thing as "infinitely" long. Not in physical reality, but in the abstract world of maths there clearly are: the sequence of real numbers is infinitely long etc. Why are you only focussing on what is possible practically?

The set of integers is 'infinite', is a figure of speech for 'has no limit' or 'has no greatest element'. If it is without a boundary/limit it cannot be measured/counted. Boundaries are the requirements that enable measurement in a world of finite entities. Math as a tool is useful when its calculations match experience. I prefer to integrate a spherical volume and apply a density factor vs counting the number of particles of mass in the sphere.

yes you can. An infinite sequence can sum to a finite number, as we have been trying to get through to you. The sum of the sequence 1 + 1/2 + 1/4 + 1/8 + ... etc sums to a finite number

The algorithm for that series is to add 1/2 of the current term as the increment to the sum S. That increment also equals the difference |Limit-S|. Thus S never terminates.

That is what you inherit with the concept of continuous division (a continuum).

Being a geometric progression, the limit will be 2. You round up the current value which approximates the limit and claim it equals the limit of 2, because no one can imagine an infinite number. Anyone can say both a 1 meter stick and a 2 meter stick have an

'infinite' number of points, but that doesn't determine which one is longer.

Therefore they are the same number, for all numbers that are not equal have a different number half-way between them.

Except integers. There is no number between 4 and 5.

The sequence .9R has no last decimal position, (because it has been defined as such), so it never terminates.

I'm not making an abstraction real, and I am using infinity as a concept, not a number.

I mean using 'infinity' for measurement AS IF it's a number, which are abstractions.

Number is a concept. So are all the means of representation originating in the mind.

Mental images are real even if they only exist in the mind.

No I'm not. Maths requires no element of time. Humans do to perform mathematical functions, but maths itself requires no element of time. 2+2=4 requires no time to be correct, only for humans to do the sum. So no contradiction.

You stated:

"Maths doesn't require "

time"."

"One can sum an infinite sequence in

seconds."

Sure looks like it.

In the abstract world of maths, in this example there is a series of infinite oscillations, and they are completed in a finite time. Real world physics need not be applied. It is conceptual / abstract. It is maths.

Then it it's fiction.

Nope, I've given you all the information you need to come up with the answer I gave.There is no "equilibrium" in the maths I gave. Just an infinite series of bounces, all complete in a finite time. That's maths for you. Your insistence on only considering real-world applications is doing you no favours.

Then your math is for entertainment and is classified as 'recreational math'.