Cantor was Wrong

Two trains, A and B, on an infinite journey.
They are on parallel tracks, starting @ the same time and traveling the same speed> 1 mile / min. Their energy is supplied by "the force" and is unlimited.
Every mile there is a brass ring.
Train A hooks a brass ring every mile. Train A's collection is depicted by the set {1,2,3,4,5,...}
Train B hooks a brass ring every 2 miles. Train B's collection is depicted by the set {2,4,6,8,10,...}
Each train has an accountant and each track also has an accountant.
After a 10 hours each set is counted. If my detractors are correct I would expect to see all four accountants reach the same count.
Train A's set has 600 members in its collection (set)
Train B's has 300
The first ten miles of track A's rings are gone. Nothing in its set
Track B has 300 rings still hanging 300 members in its set
And this pattern is reproduced throughout the infinite journey.
keiths has choked up a "response":
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Two trains, A and B, on an infinite journey.
They are on parallel tracks, starting @ the same time and traveling the same speed> 1 mile / min. Their energy is supplied by "the force" and is unlimited.
Every mile there is a brass ring.
Train A hooks a brass ring every mile. Train A's collection is depicted by the set {1,2,3,4,5,...}
Train B hooks a brass ring every 2 miles. Train B's collection is depicted by the set {2,4,6,8,10,...}
Each train has an accountant and each track also has an accountant.
After a 10 hours each set is counted. If my detractors are correct I would expect to see all four accountants reach the same count.
Train A's set has 600 members in its collection (set)
Train B's has 300
The first ten miles of track A's rings are gone. Nothing in its set
Track B has 300 rings still hanging 300 members in its set
And this pattern is reproduced throughout the infinite journey.
You are talking about the equivalent of two finite sets:Infinity is a journey which consists of finite steps. My sets will remain unequal for eternity. After the first minute there will never be a point in time in which the cardinality of the two sets is the same.
keiths has choked up a "response":
There will never be a point in time in which the two sets are infinite, either.Gibberish. The point is at every point along the journey one set will always have more brass rings. Always. Forever
Your choochoo math is therefore irrelevant to the problem, which asks about the cardinality of two infinite sets.Cardinality refers to a number whereas infinity is not a number. So understanding that infinity is a journey and relativity applies we can determine the relative cardinality between two sets.
2 Comments:
At 5:01 PM, Unknown said…
Again, it's not the rate you count, it's the number of elements in each set.
If you can match up every element of one set, 1to1, with every element of another set then the sets much be the same size. Otherwise you couldn't match them up.
Simple, easy.
Nothing to do with trains or accountants or speeds you're travelling.
At 6:42 PM, Joe G said…
The post is about the number of elements in each set.
A set is a collection of things. In this case brass rings. There are 4 people wanting to collect brass rings. One is on train A, one is one Train B, one is on track A and the other is on track B.
The collection will go on forever that is what infinity refers to.
Train A's collection will always outnumber train B's collection.
That is the journey. It isn't a finite set where it is all laid down at once for you to actually count and get a number.
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