Proving R is Bigger Than N Set Elements

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The discussion focuses on proving that the cardinality of the set of real numbers, \mathbb{R}, is greater than that of the natural numbers, \mathbb{N}. It highlights Cantor's theorem, which states that no bijection exists between these two sets. A proof is mentioned that illustrates this concept through a simple idea, although it may not be immediately apparent to those unfamiliar with it. Participants express appreciation for the clarity and effectiveness of the proof. The conversation emphasizes the significance of understanding set cardinality in mathematics.
dextercioby
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that the number of elements of \mathbb{R} (seen as a set, obviously) is bigger than the number of elements of \mathbb{N} ...? :bugeye:

Daniel.
 
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Two sets have the same cardinality iff there exists a bijection between the sets. Cantor showed that there is no bijection between \mathbb{R} and \mathbb{N}. A "[URL proof[/URL] of this involves a very simple idea - simple once one has seen it, but not until then.

Regards,
George
 
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Thankyou for the reply.

Daniel.
 
Very nice. I've never seen that proof before.
 
Wow...that's good!
 

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