A Paradox about the concept of Infinity?
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Imagine that in some imaginary place there is infinity red marbles. Now imagine that for every 100 red marbles theirs 1 blue marble. So this means that theirs infinity blue marbles right? But isnt there still more red marbles than blue? Im confused
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Answer:
No, there are not more red marbles than blue marbles. If we line up all the marbles, for every red marble you place, I can place a blue marble next to it (and vice-versa). Or to use precise math language, I can create I careate a map, a 1-to-1 and onto relationship between reds and blues. So the two infinities are equal (a countable infinity like the number of integers or the number of rational numbers) even though you'd naively think there are more reds.
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Other answers
Saying that there will still be more red marbles than blue implies that there is a point at which infinity will be 'halted' and the amount of blue and red marbles counted. If there is never a point at which infinity is 'halted' to count the marbles (which there won't be, because infinity doesn't stop) that means that there will also be infinity blue marbles. And yes, there is the same amount of red and blue marbles.
Diffo
You will never know if there are more blue or red marbles because you can never end counting them. Red marbles are counted to infinity and blue marbles are counted to infinity but only more slowly. Both tallies are on a never ending and ever increasing total. It's like the difference between walking forever and running forever.
tompainsbones
Infinity is not a number but a concept. Some infinities are larger than others. There is a whole branch of mathematics devoted to ranking infinities. Infinities are related by, "Is there a rule that ties 2 infinities together in a 1 : 1 relationship?" If so, then the infinities are of the same size. If not, one is larger than the other. Start easy: Take the real positive integers (the counting numbers) 1, 2, 3, 4, 5 , 6 ........ There is an infinite number of these/ Now lets take a sub-set of the real positive integers, the even positive integers 2, 4 , 6, 8 , 10, 12 ..... There are an infinite number of these. But, which infinity is larger or are they the same size? Turns out they are the same size because we can write a rule that relates the them in a 1 : 1 relationship. The rule: Multiply a member of the real positive integers by 2 and you get a member of the even positive integers 1*2 = 2 2*2 = 4 3 * 2 = 6 4*2 = 8 5 * 2 = 10 etc. Your example is the same infinity of exactly the same size. Your rule is, "Multiply the number of blue marbles by 100 to get the number of red marbles." 1 * 100 = 100 2 * 100 = 200 3 * 100 = 300 4 * 100 = 400 etc. Now a larger infinity to really confuse you. The rational numbers are those that can be generated by a/b where a and b are intergers. The rationals are the intergers, the terminating decmal fractions and the repeating decmal fractions 6/2 = 3 an interger 3/20 = 0.15 a terminating decmal 2/3 = 0.6666666666..... a repeating decmal If we take the set of irrational decmal fractions it is larger than the set of rational decmal fractions because we can fit an infinite number of non-terminating, non-repeating decmal fractions into the cracks.
OldPilot
correct, there are an infinite numbers of both colors, and there are more red than blue. Infinity is confusing. .
billrussell42
Just think about it in terms of the numbers getting larger and larger. No matter how many reds you have, the number of blues is going to be 100 times less. 1,000 red, 10 blue 1,000,000 red, 10,000 blue 1,000,000,000 red, 10,000,000 blue 1,000,000,000,000 red, 10,000,000,000 blue and so on and so forth. Basically, don't try to treat infinity as an actual number, but treat it as a destination.
Chib
Think about this one: The older you get, the closer you are to the relative age of your parents. For instance, when you're 25, if they're 50, you're 50% their age, 50 years later, when you're 75, and they're 100, you're 75% their age. So if you could live to be infinity, you'd be the same age as your parents!
supastremph
Infinity of both sets of marbles would exist, but the red marble set would be a larger infinity than the blue marble set. There are different degrees of infinity and it is a fairly confusing topic.
AjT
As Per the Euler Series and The Riemann Hypothesis the series converge at infinity. It appears confusing but this is what happens at infinity. When it comes to infinity it defies common sense.
goring
I'm thinking you have lost a few marbles.
Eddie
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