Infinity:The headstart paradox

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Alpha and 0mega

Junior Member
Messages
88
Infinity:The headstart paradox

Alrite,say,man A and man B wanted to have a race.So man A give man B a headstart cos man A is twice as fast as man B.When man B ran 10m,man A started running,the distance between them was 10m,after which the distance between them was reduce to 5m becos man A was twice as fast.then the distance was reduce to 2.5m,125cm,62.5cm,31.25cm and so on.if u were to keep on dividing the distance between them,its not gonna end,its infinite.So its seems that man A will never overtake man B.
 

JediStryker

Member
Messages
254
Re: Infinity:The headstart paradox

That analogy is not really accurate. Man A would eventually overtake and get past Man B. If Man A were running at 10mph (yes, that's really damn slow, I'm trying to keep this simple) and Man B were running 5mph, then Man B would have been running for 2 hours to get to the 10m mark. Man A would then start. He would reach the 10m mark in 1 hour, in which Man B has gone another 5m, making his total 15m. In another hour, both men would have reached the 20m mark, and in another hour, Man B would be at 25m while Man A was at 30m.

The concept you're talking about is a true one; there are an infinite amount of numbers between each number. But that does not translate to the "real world" in any meaningful way that I can see.
 

Zoomerz

Member
Messages
220
Re: Infinity:The headstart paradox

<div class='quotetop'>QUOTE(\"Alpha and 0mega\")</div>
Alrite,say,man A and man B wanted to have a race.So man A give man B a headstart cos man A is twice as fast as man B.When man B ran 10m,man A started running,the distance between them was 10m,after which the distance between them was reduce to 5m becos man A was twice as fast.then the distance was reduce to 2.5m,125cm,62.5cm,31.25cm and so on.if u were to keep on dividing the distance between them,its not gonna end,its infinite.So its seems that man A will never overtake man B.[/b]
Unless you modify the condition so that man B reduces his speed in relation to man A over time, man B will certainly pass man A.

Z-
 

Harte

Senior Member
Messages
4,500
Re: Infinity:The headstart paradox

<div class='quotetop'>QUOTE(\"Alpha and 0mega\")</div>
Alrite,say,man A and man B wanted to have a race.So man A give man B a headstart cos man A is twice as fast as man B.When man B ran 10m,man A started running,the distance between them was 10m,after which the distance between them was reduce to 5m becos man A was twice as fast.then the distance was reduce to 2.5m,125cm,62.5cm,31.25cm and so on.if u were to keep on dividing the distance between them,its not gonna end,its infinite.So its seems that man A will never overtake man B.[/b]

A&O,

You have here a variation on an ancient paradox. The Greek Xeno was the first to voice this paradox, at least as far as we know, thus it is called "Xeno's paradox." Xeno's example (slightly less complicated than yours, therefore better for illustrative purposes) was a man walking toward a wall. First the man had to cover half the distance to the wall, then half of that, then half of that, etc. This proves that all motion is impossible. As Iggy would say, the answer is calculus.

Let d = distance to wall at start, then at the halfway points, the succesive distances to the wall are:
d/2, d/4, d/8, d/16, etc.

We can form the sum d/2+d/4+d/8+d/16+...d/2^n = d (where n=>1->infinity)

Calculus was invented for problems like these. The concept of limit (lim) allows you to bridge that last gap, as it were.

You can see that 2^n gets larger as n gets larger. You then should know that d/2^n gets smaller and smaller as n gets larger. In the limit, where n has reached infinity, d/2^n becomes zero, that is, the distance to the wall at the limit is zero, you have reached the wall.

This is a mathematical construct. It is a way to make mathematics match up with what we observe in the real world. It by no means suggests that infinity is an actual place or that anything can become infinitesimally small. Notice that both your statements and Xeno's begin with mathematics, then go on to show how mathematics cannot describe the real world. Calculus was invented to describe what we observe in the real world. No branch of mathematics can explain what we observe in the real world.:huh:

H
 

Harte

Senior Member
Messages
4,500
Re: Infinity:The headstart paradox

<div class='quotetop'>QUOTE(\"JediStryker\")</div>
Very well explained, Harte.[/b]

Jed,

Thanks for the kindness, I was a math major, but it is A&O that deserves the praise. And I have done so in other threads.

He shows an excellent grasp of logic and reality for a 13 year old.

H.
 

StarLord

Senior Member
Messages
3,187
Re: Infinity:The headstart paradox

I am surprised that Iggy hasn't popped in here yet. He has this kind of 'radar' when it comes to formula.
 

Alpha and 0mega

Junior Member
Messages
88
Re: Infinity:The headstart paradox

<div class='quotetop'>QUOTE(\"Harte\")</div>
Jed,

Thanks for the kindness, I was a math major, but it is A&O that deserves the praise. ?And I have done so in other threads.

He shows an excellent grasp of logic and reality for a 13 year old.

H.[/b]
:);):lol::blush:
 

Chronodynamic Jim

Junior Member
Messages
116
Re: Infinity:The headstart paradox

<div class='quotetop'>QUOTE(\"Harte\")</div>
Jed,

Thanks for the kindness, I was a math major, but it is A&O that deserves the praise. And I have done so in other threads.

He shows an excellent grasp of logic and reality for a 13 year old.

H.[/b]

Is he 13? ;)
 

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