Zeno's Paradox-Series on Infinity Part 1

Zeno's Paradox is an early (ancient Greece) confrontation with infinity and infinitesimal. It took around 2,000 years to resolve the paradox, using the methods of modern (post 1850) calculus. This video shows the paradox; a later one will explain it with calculus ideas.

Infinity and infinitesimal are difficult concepts to apply to mathematics, producing a number of surprising results and observations. This video is part 1 of a series dedicated to discussing some of these ideas in layman's terms.

I spelled his name Xeno in the video, but apparently Zeno is the more common spelling.

Category:

Education

Tags:

• math
• Zeno
• paradox
• Xeno
• series
• infinity
• infinitesimal

[JayGatsbyOdysseus]

The universe is expanding .8 C (speed of light) beyond the outter most reaches.  Where and when does it stop? I don't think it does. This proves our consciousness moves beyond death. Death is like a hiccup, a cosmic speed bump, where uniform motion meets some turbulance and there is light dilation and length contraction. He should show the calculus for this hiccup to show how we get beyond 1. This is the speed bump into the next realm, a different dimension, the door.

[HIONH]

The paradox and all the infinity paradoxes of this kind are actually rejected by the atomic theory of Democritus. Mankind didnt had to wait for calculus, sorry!

[knowitall23]

Very interesting. Hope I can find the solution video

[soslothful]

I thought it was a fine looking turtle.

[MisterrLi]

By adding 1/2, 1/4, 1/8... you will get 1 in the end ONLY if you disregard the

infinitesimal difference between the sum and 1, as the standard real numbers

are defined to do. They are Dedekind complete, which means that infinitesimal

differences are neglected from the real numbers. If you use hyperreal numbers

that include infinitesimals, the sum of 1/2, 1/4, 1/8... will not reach 1. Just wanted

to make this clear, as geometry is not necessary about standard real numbers.

[lTHRICEl]

I know what you mean when you say it is cool that these thinkers were discussing these ideas at the time. I felt as if these philosophers were scratching the surface of quantum physics in a way, but of course did not know it. lol

[mechkapechka]

1 thing i don't get please someone explain to me how he gets from 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + .... and so on how did he gets 1 ?

[SMWTas]

So, does this mean I shouldn't ever buffer?  :P

[zadeh79]

Actually, what your looking at is an example of einstein's relativity. Pretty damn interesting.

[RUL1S88]

Nothing is true. Everything is forbidden.