Paradoxes

Originally posted by ArnoldSideways
This paradox concerns numbers. Each number is expressed as words with a certain number of syllables (e.g. "four" has one syllable, "se-ven" has two). Imagine the smallest number which cannot be expressed in less than twenty syllables.

This expression "the smallest number which cannot be expressed in less than twenty syllables" however contains on ...[text shortened]... essed in less than twenty syllables can indeed be expressed in less than twenty syllables.

The expression "the smallest number which cannot be expressed in less than twenty syllables" does not express the number, merely a description of the number. How about "the smallest number which cannot be expressed in fewer than twenty syllables"? 😉

Well, heres a few more:
Dichotomy Paradox: If one must travel a distance "d", then one must travel "d/2". But for one to do THAT, one must travel "d/4", "d/16", and so on. If this is the case, how must one start travelling?
Achilles and the turtle: A turtle was given a head start in a race against Achilles. All should know that Achilles would surpass the turtle in a race, but if it was thought out mathematically, it would be rather hard. By the time Achilles reaches up to the turtle, the turtle would have gone forward some distance. Achilles would then try to reach THAT point, but then the turtle would also have gone on some more distance. How does Achilles every beat the turtle then?

http://mathworld.wolfram.com/ZenosParadoxes.html

Originally posted by shyrazn155
Well, heres a few more:
Dichotomy Paradox: If one must travel a distance "d", then one must travel "d/2". But for one to do THAT, one must travel "d/4", "d/16", and so on. If this is the case, how must one start travelling?
Achilles and the turtle: A turtle was given a head start in a race against Achilles. All should know that Achilles would surpass th ...[text shortened]... Achilles every beat the turtle then?

http://mathworld.wolfram.com/ZenosParadoxes.html

All that stopping and starting, stopping and starting... no wonder Achilles had sore heels.