I have a paradox about infinity, which makes me confused. We accept that there are limitless numbers between 0 and 1. If we want to draw a line from zero to one, we will reach point 0.5 firstly. Each last half of the way has always another half-way, which means we never reach point 1 theoretically. However, we can do that in practice because nothing is continuous, but in discrete packets as the quantum mechanics claimed. Then every way has the last step, last packet due to infinity's nonexistent actually for any situation (includes cosmos) until someone gives a reasonable example.
I would appreciate if someone clears my confision.
What you are describing is not a paradox but only an impracticable way to reach position 1.0. Selecting steps like values in a geometrical series is possible but meaningless. Leibnitz and Newton already have solved this kind of paradoxes more than 300 years ago with their differential calculus.
Dear Suma,
You have no confusion. The problem you describe is also the problem of the coast, both are solved mathematically using what you call precision (I call Zoom) as if it were one more dimension. Thus, to get from one point to another starting from going halfway down each time, it is solved by establishing that Zoom level as meters, atoms, Plank length, etc. as needed.
If you are interested in the universe limits, see here how they are calculated:
http://dx.doi.org/10.13140/RG.2.2.19090.27846
I will explain it better ..
To go from a point A to a point B you have to know the position of A (given by its 4 dimensions) and the position of B (also given by its 4 dimensions) As this 4 dimension is the Zoom (for all intents and purposes it is indistinguishable from time) you already have the precision necessary to go from A to B
Firstly thank you very much to Sergio Garcia Chimeno and Wolfgang Konle for your reply.
In conclusion, can we say that infinity is existed or is it just a theoretical value which is unmeasurable ?
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