Ibn Taymiyyah wrote:Deep inside I know that there is something wrong with this argument but I can’t put my finger on it.
ibn taymiyyah wrote:* There are infinite numbers between the 1 and the 2 and between the 2 and the 3 … this proves that more than one (linear) infinity exist at the same time.
threewood14 wrote:Who is Zeno?
1) We cannot imagine two objects that are infinite in size to be anything but equal in size.
2) If a relatively small object increases in size at a constant daily rate (10 units of size per day), and,
3) A larger object increases in size at the same constant rate.
4) If both objects begin increasing in size at the same time, we can’t imagine the smaller object ever catching up with the larger object. There will never come a time when they become equal.
5) Therefore they will never become infinite in size because they will never become equal (point (1)).
It doesn't matter if we can 'imagine' them catching up in size. infinity is not something you can add numbers to get to.
Ibn Taymiyyah wrote:5) Therefore they will never become infinite in size because they will never become equal (point (1)).
Deep inside I know that there is something wrong with this argument but I can’t put my finger on it.
Ibn Taymiyyah wrote:1) We cannot imagine two objects that are infinite in size to be anything but equal in size.
Here is one of Canor's observations: Imagine the set N of all natural numbers (1,2,3,4,5,6.....). Now eliminate all the even numbers, so we are left with set O=(1,3,5,7,9...). Common sense tells you that set O is half as big as set N, right? But both O and N are still "infinite in size," even though we removed every other item from set N to get set O. In fact, for every item in N, we can find another item in O to pair it with, as if they were equal in size. Weird, huh?
threewood14 wrote:you gotta remember this about infinity. look at a ruler. how much space is between the one unit mark and the 2 unit mark. if you are using metric, probably about 1cm. now look at it this way. how many point in space time are between those two lines. well first of all, a point in space time is infinitly small. therefore, there are an infinite amount of points in space time between those two objects. we always look at our surroundings at human intervals. now take time. how many point in time are in one second. infinite right? one second is just a measurement of time at the rate we humans experience it.
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threewood14
mercutio wrote:threewood14 wrote:you gotta remember this about infinity. look at a ruler. how much space is between the one unit mark and the 2 unit mark. if you are using metric, probably about 1cm. now look at it this way. how many point in space time are between those two lines. well first of all, a point in space time is infinitly small. therefore, there are an infinite amount of points in space time between those two objects. we always look at our surroundings at human intervals. now take time. how many point in time are in one second. infinite right? one second is just a measurement of time at the rate we humans experience it.
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threewood14
Reminds me of that drunken clown Zeno & his paradoxes, the arrow one this time. To go from a to b it must past through c, to go from a to c it must pass through d, to go from a to d it must go through e, blah blah blah ad infinitum et absurdum. Therefore the arrow can never arrive at b because there are an infinite amount of points it must pass through before it gets there. Are you right, Mr Zeno, are you right? No, you are wrong. Why? Because if you were alive I would shoot an arrow at you & it would not pass through an infinite amount of points & never hit you, it would hit you & you would die. Again. RIP.
threewood14 wrote:Here is something that is mind boggling. If something moves an infinite small distance, it would take an infinite amount of time for it to get from point A to point B whereever they may be. Let us say that we give it 100 years to move one inch. Since the distance it is moving is infinitly small, it would obviously not get there by then. But, it would have not moved at all. Because an infinitely small distance plus an infinitely small distance equals and infinitly small distance. If it did move a distance, then it would take a finite amount of time to get from a to b. But since it doesn't, an infinitly small distance can be thought of as 0!!
Democritus wrote:You cannot ever "reach" infinity.
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