Do you know any paradox's that have to do with Infinity?

Question

The only one I know is that it is impossible to travel from point A to point B because you have to travel half of the distance first... then half of that distance... and half of that... and half of that... etc... and therefore you cannot actually get to point B

Answer 1

You're talking about Zeno's second paradox of motion. There are loads of summaries of it on the Net so I won't bother giving you mine. There are actually a number of solutions to it. (Aristotle himself dispells the paradox in book 6 of his Physics)

There are several other infinity paradoxes:

Cantor's Paradox:
The set of all sets is both the biggest set of all and not the biggest set of all.

Galileo's Paradox:
There are no more postive integers than there are squares of positive integers.

Hilbert's Hotel
The set of all positive integers is no more numerous than the positive integers greater than 1.

The Tristram Shandy Paradox:
Great name! A variation on Zeno's Paradox described by Bertrand Russell.

There's no space here to explain these properly. Wikipedia's maths and logic articles are usually pretty reliable, but you can Google these paradoxes too....

Answer 2

Yes. I know the one you're talking about. It is one of Zeno's Paradoxes. It says that:

Suppose you have to travel a distance, from A to B.

Also suppose, you always walk half the distance left. If you keep doing this, you'll NEVER get to point B.

Zeno also has other paradoxes. Another one of his is "Achilles and the Tortoise."

In the paradox of Achilles and the Tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is such a fast runner, Achilles graciously allows the tortoise a head start of a hundred feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise's starting point; during this time, the tortoise has "run" a (much shorter) distance, say one foot. It will then take Achilles some further period of time to run that distance, in which said period the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, Zeno says, swift Achilles can never overtake the tortoise. Thus, while common sense and common experience would hold that one runner can catch another, according to the above argument, he cannot; this is the paradox.

Answer 3

Not a paradox but a new definition of infinity. In the forming of a black hole it starts collapsing and the gravity accelerates the pieces and as the accelerate their velocity approaches the speed of light . As the speed approaches the speed of light it will start to increase the mass which increased the gravity pull and acceleration until it reaches the speed of light at which time the mass becomes infinity. This can create a gravity well that may be 100 light years across.

Answer 4

Here is another "infinity-related" paradox: there must be "different sizes" of infinity, even though they are all infinite! Consider the set of all odd numbers (1,3,5,7..and so on to infinity); for each member of this set, there is an even number one digit bigger than it (2,4,6,8...etc), which proves these two sets are the same size. If you mix them both together you get the set of all whole numbers, which must be TWICE as big as either the set of all even numbers or the set of all odd numbers!

Now my head hurts!

Answer 5

If you stay at the point A and look at the point B(+ infinity) and then turn backside look at again the point B ( - infinity) and what you can see the same point,they said.

Answer 6

Can you fill an infinite Universe with infinite matter?

That was "Zeno's Paradox" you mentioned, by the way. Here's more on it, including a "Thompson's Lamp".

http://www.mathacademy.com/pr/prime/articles/zeno_tort/

Answer 7

quantum mechanics explains alot of paradox's. such as if i went back in time, and shot myself, i would still exist. but the 'me' i shot in the past is from a parallel dimension, and in their reality, they would be dead. weird stuff eh!