Infinity is good as a concept. Some people used it enough that they created a placeholder for it.
Though in the real word the universe is quantized. It is all measured in units, it is useful. Infinity doesn't help solve problems in the universe. If you need to use infinity to solve a problem, then you're asking the wrong questions. It's just my view. I see no use for it in most cases.
You use real examples to make a point. I get the idea, but see too many problems at the basic level. All I see are units. The universe does not have infinite resolution. In the end there are bits, 0s and 1s, existent or non-existent. So I don't think the universe is programmed to support a variable called “infinity”. The universe is made up of rules and laws. Why use infinity when you can use something more exact.
As far as being boolean, as in being a unit of 1 or 0...isn't this known as quanta? The universe is made of measurable amounts of energy. It is measurable. Infinity is not. I guess infinity could be used as a “don't care/unknown” bit.
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Once you understand that its infinitely reflective *unidirectional* geometric series of "vortex like (spinning)" conic rays towards a point in space, or a surface like your mirror, that fades (compresses) into a point that merges, because all the images when you look off into that "hall of mirrors" you've just created merges into an area (a completely filled space near the "Vanishing point" (the point where objects lose their boundaries and become unbounded)), all the images created from that eternal reflection, at some point become squished together "infinitely" (completely filled) where no object is distinguishable from any other object: all objects merge and lose their boundaries! (That is to lose distinction or boundedness)
If the reflection gets small enough there will be a limited number of photons left. The photons that are left will represent a few different units of energy, That will be the end of the “infinite picture creation loop”. The real world gets in the way. Data gets dropped. Not enough resolution.
In a final attempt at understanding infinity, I mentally overclocked my brain, but all I got were cold chills and corrupted data, along with a really nice light show of dots and lines in my minds eye. It does not compute. After 25 seconds of intense focus, which is an infinity for me, I decided to give up (Is infinity relative?). But then, I'm just a technician that couldn't focus enough to get through the calculus requirements of engineering. I remember calculus had a lot more infinity variables, so I stuck to algebra and trig.
I like fractals. That's probably the closest I can get to seeing and understanding infinity in the real world. There are fractals everywhere.
Change the binary units to trinary logic and the positive and negative data space cancels itself out to nothingness. Therefore infinity is nothing. Symmetry solves infinity, reducing it to nothingness. Nothing can be measured as a lack of one. Therefore it is not infinite. A lack of one can only be infinite if the number of ones are infinite. Since one can be measured as a unit, infinity cannot exist. I'm not making any sense any more. Time to stop.