Mathematical Paradox

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Ever heard of this problem?

Let us a assume a frog jumps half a distance to it's destination. Therefore, its jumps would account as: 1/2 the distance + 1/4 the distance + 1/8 the distance and so forth.

Essentially, 1/2n

Would it ever reach its destination? Well I have computed that formula numerous amount of time and mathematically, it always results as impossible to reach.

Or perhaps not...

Some theoretical mathematicians have argued theoretically, after a googleplex of times, the destination would be reach as the resulting step is a positive integer. Infinitely small, yes, but nevertheless a positive integer.

Do the same laws of mathematics still apply when one reaches an enormous, unfathomable value?

Please discuss.

I'd be curious to see their theory or how they came to that conclusion. Logically, it's not a paradox and could only equal the final distance if the .000000000015 were rounded up to .000000000002. No matter the number you start with, and no matter how many hops, the frog will never get closer than a sliver away.

Meisner spaces are claustrophobic...

_________________
"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos

However at what point might the frog be splined back into tadpoles? I suppose I might never know how many cubits a frog needs to hop before it becomes a poisonous frog, ultimately it's almost like this question suggests the transitive property is all that's necessary for the existence of life.

_________________
"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos

This is just a variant on the 2500 year old "Zeno's Paradox" from ancient Greece.

Forget about frogs hopping. Just use yourself walking, or driving a car. The same thing applies.

Lets say you wanna get from your sofa to the fridge: you first have to reach the point halfway between your sofa and the fridge. But before that you have to reach the point halfway between your sofa and that halfway point, but before that you hafta reach the point halfway between your sofa and that second halfway point (the quarterway point), but before that...and so on. You would have to hit every point between the sofa and the fridge. And since there are an infinite number of geometric points along the line between your sofa and the fridge (just like there are an infinite number of points on any line) it would take an infinite time to accomplish that. Which means you cant move from your sofa to the fridge. Indeed ALL motion is an illusion. There is no motion. Nor time itself. That according to the ancient Greek philosopher Zeno in 490 BCE.

According to theoretical physics the smallest finite length is the Plank length which is approximately 1.616199x10^(-35) metres. That is the smallest finite distance possible, according to theoretical physics.

Let 0 be the starting line and 1 be the finish line. Let,

s_n=1+1/2+(1/2)^2+...+(1/2)^n

There exists a cardinal number n such that the frog, theoretically, has to touch the finish line. I'll work out this number.

Using the partial geometric sum formula (which is easy to prove by mathematical induction or other methods),



The cardinal number n such that the frog would theoretically have to touch the finish line is abotu 116.

Phenomena portraying absolute series strikes me as the computational singularity, anything can be in-vivo vivisected to Planck depth provided the scientists with the funding manage to stay there rather than using all that same equipment for cryptographic brute-force exploits. Are we examining the sum wave state of Zeno & Euclid?

_________________
"Standing on a well-chilled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origin of the worlds."
-Georges Lemaitre
"I fly through hyperspace, in my green computer interface"
-Gem Tos

I watched a V Sauce on this very issue back in early December. Worth watching if any of you haven't