Imagine I count in two ways
The first is 1, 2, 3, 4, 5 ….
The second is 1.1, 1.2, 1.3, 1.4, 1.5 ….
Could I argue that the second way of counting actually proves that the second infinity is bigger than the first?
AiY
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Infinity
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AsleepInYorkshire
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Re: Infinity
No. This is a well-known question, and well-understood amongst mathematicians. You can set up a correspondence between your sequences such that every new number in one maps directly to a new number in the other.
Having said that, Cantor's maths tell us there is indeed an infinite hierarchy of ever-bigger infinities. For further research, you could start with some of the terms mentioned in viewtopic.php?f=73&t=15398 .
Having said that, Cantor's maths tell us there is indeed an infinite hierarchy of ever-bigger infinities. For further research, you could start with some of the terms mentioned in viewtopic.php?f=73&t=15398 .
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