A Paradox

[RodReynolds 87]

After thinking about this problem, I will now show how the OP is indeed wrong about this problem. Forgive my notation, I'm limited here.The OP did a good job of confusing everyone here by making time fundamental to the problem. Time always confuses people, but you dont have to set up the problem that way. All the problem tells us is that we have an infinite sequence and gives us constraints on money and time. I'm guessing the OP never set up any equations for this problem because when you do, the answer is obvviousSo you can see that at infinity eventhough time does converge to 1, the amount of money we have approaches infinity. This does NOT show that infinity doesnt exist (as the OP claimed).I'm guessing the OP got his paradox mixed up. The real paradox is that if m2>m1 at any specific point, then why are they equal at infinity? If you've taken any type of math theory you've seen this type of discussion before. Its simliar to the "is infinity+1>infinity" debate (in our case its m1 = inf < 6*inf = m2 debate) and there's a lot of math theory on this stuff. This type of stuff is over my head, but i'll give it a shot. Infinity isnt really a measurable value in the real world sense. Its a little more abstract. So the statment m1 = inf < 6*inf = m2 doesnt really make sense. The best thing to say is that m1 and m2 are equivalent.

You did a good job here. You are basically putting into a more mathematical form the explanations already given. Please note, I admitted earlier that my statement "infinity does not exist" was better explained by Petoria, who I think said basically what you said. I have admitted that there is no such paradox, but it is an apparent paradox at first glance, one which I found somewhat interesting. I have admitted that the real problem is (did you read the entire thread btw?) trying to fit an infinite sequence of events into a finite time period. It is of course impossible to look at the problem in a post 1 second world as though you completed the task assigned. Edit: I'm getting more confused as I think about this. I'm just reading what Wikipedia has to say about Zeno's paradoxes, and I guess the essence of this problem is this: Is it logically possible to complete an infinite number of tasks? If time and space is continuous, you presumably do it all the time, example: You walk a meter, but to do that, you first have to walk half a meter, then you walk a quarter of a meter, then an eighth, etc. Of course, this won't take an infinite amount of time, as the amount of time will decrease with each step. You can get an infinite series which converges to some value. However, you still have to complete an infinite number of tasks, is this logically possible. I'm just going to quote straight from Wikipedia, my new god, for an interesting discussion."A problem with using calculus to try and solve Zeno's paradoxes is that this only addresses the geometry of the situation, and not its dynamics. What is at the core of Zeno's paradoxes is the idea that one cannot finish the act of sequentially going through an infinite sequence, and while calculus shows that the sum of an infinite number of terms can be finite, calculus does not explain how one is able to finish going through an infinite number of points, if one has to go through these points one by one. Indeed, saying that there are an infinite number of points or intervals within some finite interval is of course the very assumption in the Achilles and Dichotomy Paradoxes, and it is this assumption regarding the geometry of the situation that leads to a paradox regarding its dynamics.It should also be noted that calculus-based solutions that are offered often object to the claim that "it must take an infinite amount of time to traverse an infinite sequence of distances". However, Zeno's paradox doesn't contemplate the time it would take for Achilles to catch the Tortoise; it simply points out that in order for Achilles to catch up with the Tortoise, Achilles must first perform an infinite number of acts, which seems to be impossible in and of itself: time has nothing to do with it. Thus, calculus-based solutions to Zeno's paradoxes often make the paradox into a straw man.Some people, using the notion of a supertask, argue that an infinite number of things can be completed in sequence as follows: do the first thing in 1 second, the second in half a second, the third in a quarter, etc. Again from a calculus point of view, this would seem to mean that after 2 seconds an infinite number of things would have been done. However, there would seem to have to be a problem with this, as getting to the end of an endless series would seem to be a contradiction in terms. Indeed, the problem with this argument is exactly the same as before. Since this line of reasoning assumes that there is a one-to-one mapping between the acts and the points (or intervals) in time during which that act takes place, one would need to go through (and finish) an infinite number of points in time in order to complete the infinite number of acts to be performed. But, once again, such an infinite sequence can, by its very infinite nature, not be finished. Indeed, following Zeno's logic as we just did now, we have created yet another version of his paradox: not only does motion through space seem to be impossible, but the flow of time itself seems to be impossible as well.In short, trying to use calculus to resolve the paradox simply reaffirms the idea that space and time are infinitely divisible, and thus still suffers from the basic question as to how one can possibly reach the end of an endless series.Imagine, for instance, that at start, Achilles notes the position occupied by the turtle, and calles it first; after reaching that position, he once again notes the position the turtle has moved to, calling it second, and so on. If he catches up with the turtle in finite time, the counting process will be complete, and we could ask Achilles what the greatest number he counted to was. Here we encounter another paradox: while there is no "largest" number in the sequence, as for every finite number the turtle is still ahead of Achilles, there must be such a number because Achilles did stop counting.On the other hand, it is conceivable is that there is no reason why an infinite number of events cannot be "finished." "Finishing" a set of things means to do all of those things in a finite amount of time. If an infinite number of things can be done in a finite amount of time, then those things are all "finished." It could likewise be argued that this is exactly what the calculus solution demonstrates.In this point of view, the number of "acts" involved in anything is merely a matter of human convention and labeling. One could alternately consider the whole sequence to be one "act." Calculus demonstrates that the process takes the same amount of time and is "finished" in exactly the same way with either manner of labeling. This could be taken as evidence that the labeling of acts is arbitrary and has nothing to do with the underlying physical process being described." (http://en.wikipedia.org/wiki/Zeno's_paradoxes)

Out of curiosity, where did the OP come up with this situation?Oh and btw, I think you're looking at the problem wrong.

When I visited a friend back at the school I used to go to, he presented the problem to me and some other friends. It amused us for a few minutes, and I thought it was post worthy. I don't know where he got it though.

[screech 0]

This actually is an area of study strangely enough. The hypothesis is that time should move in some type of discrete unit, and that shortest time should be measurable. Tough to think about, but you can apply some modern theoretical physics formulae to the problem. Nothing has come out of it yet, but there is some progress.This is probably one of the most interesting things i've ever read about because of it's real-world application.

Petoria,This guy has a different theory. You can get the summary here

[Actuary 3]

this is sillyyou will always have 6x the amount of money with the 2nd scenariononetheless... both stacks are unbounded.didn't read much of thread..did it get good?

[ricker 0]

this is sillyyou will always have 6x the amount of money with the 2nd scenariononetheless... both stacks are unbounded.didn't read much of thread..did it get good?

You might've missed my little gem, or DnA's picture...that's about it

[madtrix72 0]

Fair enough. What you are in other words saying is that you can not agree to the untenable assumption of doing the infinite number of tasks in a finite amount of time, and you will not agree to it even for arguments sake. If you were to agree to it, then of course I would tell you that there is no last number of the bills that I burn. I propose a truce.

Accepted. It was fun while it lasted.

[RodReynolds 87]

You're all a bunch of dicks and I hate every last one of you.

[LongLiveYorke 38]

I hate Zeno's paradox, for the record.

[hank213 1,823]

[navybuttons 15]

I hate Zeno's paradox, for the record.

i wanted to ask someone this and you seem pretty likely to know.does the universe have infinite space? if it does then how can it be growing? if it doesn't then what lies beyond the edge of the universe?how is the universe shaped? is it like a ball? is it like a donut?do i like donuts? please make the answers simple and in layman's terms as i am an idiot. thank you.

[Dirtydutch 8]

i wanted to ask someone this and you seem pretty likely to know.does the universe have infinite space? if it does then how can it be growing? if it doesn't then what lies beyond the edge of the universe?how is the universe shaped? is it like a ball? is it like a donut?do i like donuts? please make the answers simple and in layman's terms as i am an idiot. thank you.

Here it is, plain and simple, but written in binary 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[ShakeZuma 585]

Here it is, plain and simple, but written in binary code:010010000110000101101000011000010110100001100001001011000010000001001001001000000110010001101111011011100010011101110100001000000110000101100011011101000111010101100001011011000110110001111001001000000110101101101110011011110111011100100000011100110110100001101001011101000010000001100001011000100110111101110101011101000010000001110100011010000110100101101110011001110111001100101110001000000100001001110101011101000010000001101000011001010111001001100101001000000110000101110010011001010010000001110100011010000110010100100000011011000111100101110010011010010110001101110011001000000111010001101111001000000110110101111001001000000110011001100001011101100110111101110010011010010111010001100101001000000100100001100001011011000110110000100000011000010110111001100100001000000100111101100001011101000111001100100000011100110110111101101110011001110011101000001101000010100000110100001010010110010110111101110101001001110111001001100101001000000110000100100000011100100110100101100011011010000010000001100111011010010111001001101100001011000010000001100001011011100110010000100000011110010110111101110101001001110111011001100101001000000110011101101111011011100110010100100000011101000110111101101111001000000110011001100001011100100010000000001101000010100100001101100001011101010111001101100101001000000111100101101111011101010010000001101011011011100110111101110111001000000110100101110100001000000110010001101111011011100010011101110100001000000110110101100001011101000111010001100101011100100010000001100001011011100111100101110111011000010111100100100000000011010000101001011001011011110111010100100000011000110110000101101110001000000111001001100101011011000111100100100000011011110110111000100000011101000110100001100101001000000110111101101100011001000010000001101101011000010110111000100111011100110010000001101101011011110110111001100101011110010010000000001101000010100101100101101111011101010010000001100011011000010110111000100000011100100110010101101100011110010010000001101111011011100010000001110100011010000110010100100000011011110110110001100100001000000110110101100001011011100010011101110011001000000110110101101111011011100110010101111001001000000000110100001010010010010111010000100111011100110010000001100001001000000110001001101001011101000110001101101000001000000110011101101001011100100110110000101100001000000110001001110101011101000010000001101001011101000010011101110011001000000110011101101111011011100110010100100000011101000110111101101111001000000110011001100001011100100010000000001101000010100100001101100001011101010111001101100101001000000111100101101111011101010010000001101011011011100110111101110111001000000110100101110100001000000110010001101111011011100010011101110100001000000110110101100001011101000111010001100101011100100010000001100001011011100111100101110111011000010111100100100000000011010000101001010011011000010111100100100000011011010110111101101110011001010111100100101100001000000110110101101111011011100110010101111001001000000111011101101111011011100010011101110100001000000110011101100101011101000010000001111001011011110111010100100000011101000110111101101111001000000110011001100001011100100010110000100000011001110110010101110100001000000111100101101111011101010010000001110100011011110110111100100000011001100110000101110010001000000000110100001010000011010000101001000001011011100110010000100000011001000110111101101110001001110111010000100000011110010110111101110101001000000110101101101110011011110111011100101100001000000110010001101111011011100010011101110100001000000111100101101111011101010010000001101011011011100110111101110111001000000000110100001010010101000110100001100001011101000010000001101001011101000010011101110011001000000111011101110010011011110110111001100111001000000111010001101111001000000111010001100001011010110110010100100000011101110110100001100001011101000010000001101000011001010010011101110011001000000110011101101001011101100110100101101110011001110010000001111001011011110111010100100000000011010000101001010011011011110010000001100110011000010111001000100000011001110110111101101110011001010010000001101111011011100010000001111001011011110111010101110010001000000110111101110111011011100010000000001101000010100100001001110101011101000010000001111001011011110111010100100000011000110110000101101110001000000110011101100101011101000010000001100001011011000110111101101110011001110010000001101001011001100010000001111001011011110111010100100000011101000111001001111001001000000111010001101111001000000110001001100101001000000111001101110100011100100110111101101110011001110010000000001101000010100100001001110101011101000010000001111001011011110111010100100111011011000110110000100000011011100110010101110110011001010111001000100000011000100110010100100000011100110111010001110010011011110110111001100111001000000110001101100001011101010111001101100101001000000000110100001010000011010000101001011001011011110111010100100111011100100110010100100000011000010010000001110010011010010110001101101000001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01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010111 01100001 01110100 01100011 01101000 00100000 01101111 01110101 01110100 00100000 01100010 01101111 01111001 00100000 01110011 01101000 01100101 01101100 01101100 00100000 01100011 01101000 01100101 01110111 00100000 01111001 01101111 01110101 00100000 01110101 01110000 00001101 00001010 01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010011 01101000 01100101 01110011 00100000 01100001 00100000 01101101 01100001 01101110 01100101 01100001 01110100 01100101 01110010 00001101 00001010 01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010111 01100001 01110100 01100011 01101000 00100000 01101111 01110101 01110100 00100000 01100010 01101111 01111001 00100000 01110011 01101000 01100101 01101100 01101100 00100000 01100011 01101000 01100101 01110111 00100000 01111001 01101111 01110101 00100000 01110101 01110000 00001101 00001010 01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010011 01101000 01100101 01110011 00100000 01100001 00100000 01101101 01100001 01101110 01100101 01100001 01110100 01100101 01110010 00001101 00001010 00001101 00001010 01111001 01100101 01100001 01101000 00101100 00100000 01001001 00100000 01100010 01101111 01101111 01101011 01101101 01100001 01110010 01101011 01100101 01100100 00100000 01110100 01101000 01100001 01110100 00100000 01110011 01101001 01110100 01100101 00100000 01110100 01101111 01101111

[Dirtydutch 8]

01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010111 01100001 01110100 01100011 01101000 00100000 01101111 01110101 01110100 00100000 01100010 01101111 01111001 00100000 01110011 01101000 01100101 01101100 01101100 00100000 01100011 01101000 01100101 01110111 00100000 01111001 01101111 01110101 00100000 01110101 01110000 00001101 00001010 01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010011 01101000 01100101 01110011 00100000 01100001 00100000 01101101 01100001 01101110 01100101 01100001 01110100 01100101 01110010 00001101 00001010 01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010111 01100001 01110100 01100011 01101000 00100000 01101111 01110101 01110100 00100000 01100010 01101111 01111001 00100000 01110011 01101000 01100101 01101100 01101100 00100000 01100011 01101000 01100101 01110111 00100000 01111001 01101111 01110101 00100000 01110101 01110000 00001101 00001010 01001111 01101000 00100000 01101000 01100101 01110010 01100101 00100000 01110011 01101000 01100101 00100000 01100011 01101111 01101101 01100101 01110011 00001101 00001010 01010011 01101000 01100101 01110011 00100000 01100001 00100000 01101101 01100001 01101110 01100101 01100001 01110100 01100101 01110010 00001101 00001010 00001101 00001010 01111001 01100101 01100001 01101000 00101100 00100000 01001001 00100000 01100010 01101111 01101111 01101011 01101101 01100001 01110010 01101011 01100101 01100100 00100000 01110100 01101000 01100001 01110100 00100000 01110011 01101001 01110100 01100101 00100000 01110100 01101111 01101111

0100001001101001011011100110000101110010011110010010000001100011011011110110111001110110011001010111001001110100011001010111001001110011001000000110000101110010011001010010000001100001011011000110110000100000011011110111011001100101011100100010000001110100011010000110010100100000011100000110110001100001011000110110010100101110001000000100011001101111011100100010000001110011011010000110111101110010011101000010000001100011011011110110010001100101001000000110100101110100001001110111001100100000011001100111010101101110001000000111010001101111001000000110010001101111001000000110100101110100001000000110001001111001001000000110100001100001011011100110010000101100001000000110001001110101011101000010000001100110011011110111001000100000011101000110100001100001011101000010000001001001001000000110101001110101011100110111010000100000011101010111001101100101011001000010000001110100011010000110010100100000011011110110111001100101001000000110001001110101011010010110110001110100001000000110100101101110011101000110111100100000010011000110100101101110011101010111100000101110

[ShakeZuma 585]

0100001001101001011011100110000101110010011110010010000001100011011011110110111001110110011001010111001001110100011001010111001001110011001000000110000101110010011001010010000001100001011011000110110000100000011011110111011001100101011100100010000001110100011010000110010100100000011100000110110001100001011000110110010100101110001000000100011001101111011100100010000001110011011010000110111101110010011101000010000001100011011011110110010001100101001000000110100101110100001001110111001100100000011001100111010101101110001000000111010001101111001000000110010001101111001000000110100101110100001000000110001001111001001000000110100001100001011011100110010000101100001000000110001001110101011101000010000001100110011011110111001000100000011101000110100001100001011101000010000001001001001000000110101001110101011100110111010000100000011101010111001101100101011001000010000001110100011010000110010100100000011011110110111001100101001000000110001001110101011010010110110001110100001000000110100101101110011101000110111100100000010011000110100101101110011101010111100000101110

01101111 01101000 00101110 00100000 00100000 01101110 01100101 01110010 01100100 00101110

[speedz99 145]

01101111 01101000 00101110 00100000 00100000 01101110 01100101 01110010 01100100 00101110

100010011

[Spademan 94]

I hate cyborgs.I'm hunting you now.Cyborgs.

[LongLiveYorke 38]

does the universe have infinite space? if it does then how can it be growing? if it doesn't then what lies beyond the edge of the universe?how is the universe shaped? is it like a ball? is it like a donut?

So, it's difficult to answer questions about the shape of the universe without discussing something known as a "metric." See, when we talk about the universe or anything on a very large scale, our normal ideas about space and geometry start to break down. Often scientists try to explain it using phrases such as "the universe is growing" or " the universe is shaped in a certain way," but when they do it, they're really talking about something called a metric.What, then, is a metric? The metric is the way that a person measures "distance." We are used to using what is called the euclidean metric, where the distance (in three dimensions) is given by the square root of x^2 + y^2 + z^2. This is the metric that applies to flat space-time. So, if we are working in a flat universe, then triangles have 180 degrees and we measure the distance between things using the standard Pythagorean theorem in 3-d. But the universe is not 100% flat. Gravity, according to general relativity, "curves" space and gives it a shape. Really what is happening is that gravity changes the "metric," meaning that it alters the way that distances between two places are measured. So, if the metric is altered in a way such that it is increased between two places, than effectively what we think of as "distance" between those places is increased. Just imagine that the metric is a ruler and gravity can alter the shape and length of that ruler. If the ruler gets smaller and smaller, then things measured by that ruler will be seemingly further and further apart.So, how does this apply to the universe? Well, scientists have observed that the universe is "expanding." But this really means that the metric, or the "ruler," is getting smaller and smaller. So, if we measure the distance between here and Andromeda today and it turns out to be 1,000 lengths of our ruler, and our ruler gets smaller, then tomorrow the distance we measure could be 2,000 rules, effectively making the distance longer. This is what we mean when we say the universe is expanding: the distances between every point in space is getting larger and larger.The metric can be bent as well, though. The "shape" of the universe is described by how much our ruler is "curved." Imagine that we have a ruler that is curved. Let's say that it is curved through 90 degrees (a right angle). If we measure the distance of something by putting this curved ruler end to end, then after 4 ruler lengths, the ruler will end up back where it started (in other words, the four rulers put together will form a circle). So, according to our measurement, after 4 ruler lengths in a given direction, we end up in the same spot (because the ruler, or the metric, is curved). Imagine all this on a very large scale.If the universe is curved in this certain way, then if we go out on a spaceship in a straight long for a very long distance, we eventually will return to where we are (if the straight line is defined by following along the ruler, which in this case happens to be curved).The shape of this ruler is determined by the mass density of the universe. There is a critical value for this density where if the universe is denser than this value, it will be curved one way (have negative curvature), if it is equal, it will be flat, and if it is less, it will be curved another way (have positive curvature). So, this answers some of your questions. The universe can indeed be infinite but still be growing because the meaning of growing means only that our rulers are shrinking and thus the distance between things is getting larger.Nothing lies beyond the "edge of the universe" because this concept is ill defined. If the universe is flat, it will go on forever and you will never reach an edge. If the universe is curved in a way and is finite, you won't reach an edge. Rather, eventually after going in a straight line you will end up where you started (just imagine walking on the surface of the earth in a straight line around the equator. The Earth is finite but it doesn't have an edge; you will just walk back to where you started). The possible shapes of the universe are flat (just consider a giant flat grid that goes on forever), curved like a ball (picture the Earth or any large sphere) or curved in another way that one can imagine looks like a saddle (it's hard to find an analogy for it visually, but the description of the metric is well defined).See:http://en.wikipedia.org/wiki/Shape_of_the_universe(ignore most of the math if you want)

[Dirtydutch 8]

So, it's difficult to answer questions about the shape of the universe without discussing something known as a "metric." See, when we talk about the universe or anything on a very large scale, our normal ideas about space and geometry start to break down. Often scientists try to explain it using phrases such as "the universe is growing" or " the universe is shaped in a certain way," but when they do it, they're really talking about something called a metric.What, then, is a metric? The metric is the way that a person measures "distance." We are used to using what is called the euclidean metric, where the distance (in three dimensions) is given by the square root of x^2 + y^2 + z^2. This is the metric that applies to flat space-time. So, if we are working in a flat universe, then triangles have 180 degrees and we measure the distance between things using the standard Pythagorean theorem in 3-d. But the universe is not 100% flat. Gravity, according to general relativity, "curves" space and gives it a shape. Really what is happening is that gravity changes the "metric," meaning that it alters the way that distances between two places are measured. So, if the metric is altered in a way such that it is increased between two places, than effectively what we think of as "distance" between those places is increased. Just imagine that the metric is a ruler and gravity can alter the shape and length of that ruler. If the ruler gets smaller and smaller, then things measured by that ruler will be seemingly further and further apart.So, how does this apply to the universe? Well, scientists have observed that the universe is "expanding." But this really means that the metric, or the "ruler," is getting smaller and smaller. So, if we measure the distance between here and Andromeda today and it turns out to be 1,000 lengths of our ruler, and our ruler gets smaller, then tomorrow the distance we measure could be 2,000 rules, effectively making the distance longer. This is what we mean when we say the universe is expanding: the distances between every point in space is getting larger and larger.The metric can be bent as well, though. The "shape" of the universe is described by how much our ruler is "curved." Imagine that we have a ruler that is curved. Let's say that it is curved through 90 degrees (a right angle). If we measure the distance of something by putting this curved ruler end to end, then after 4 ruler lengths, the ruler will end up back where it started (in other words, the four rulers put together will form a circle). So, according to our measurement, after 4 ruler lengths in a given direction, we end up in the same spot (because the ruler, or the metric, is curved). Imagine all this on a very large scale.If the universe is curved in this certain way, then if we go out on a spaceship in a straight long for a very long distance, we eventually will return to where we are (if the straight line is defined by following along the ruler, which in this case happens to be curved).The shape of this ruler is determined by the mass density of the universe. There is a critical value for this density where if the universe is denser than this value, it will be curved one way (have negative curvature), if it is equal, it will be flat, and if it is less, it will be curved another way (have positive curvature). So, this answers some of your questions. The universe can indeed be infinite but still be growing because the meaning of growing means only that our rulers are shrinking and thus the distance between things is getting larger.Nothing lies beyond the "edge of the universe" because this concept is ill defined. If the universe is flat, it will go on forever and you will never reach an edge. If the universe is curved in a way and is finite, you won't reach an edge. Rather, eventually after going in a straight line you will end up where you started (just imagine walking on the surface of the earth in a straight line around the equator. The Earth is finite but it doesn't have an edge; you will just walk back to where you started). The possible shapes of the universe are flat (just consider a giant flat grid that goes on forever), curved like a ball (picture the Earth or any large sphere) or curved in another way that one can imagine looks like a saddle (it's hard to find an analogy for it visually, but the description of the metric is well defined).See:http://en.wikipedia.org/wiki/Shape_of_the_universe(ignore most of the math if you want)

But, you wouldn't have enough fuel to to that, so it's a paradox!I don't understand things, sometimes.Seriously, though, interesting stuff.

[SuitedAces21 2,722]

I agree with RodReynolds.

[Jeepster80125 0]

I love the appearance of CU here.

[Dawson Leery 12]

lol with all that money just buy a fire proof safe

[timwakefield 68]

Mathematically, infinity doesnt have to be a set number, some infinities are bigger than other infinities. For instance, the cardinality of the set of all even integers is infinity, but so is the set of all integers. Clearly the set of all integers is twice as large though.

[mtdesmoines 3]

Iloveitwhenpeopleargueaboutnothingatall