Alternate Treatment of Infinity

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SUMMARY

This discussion centers on the concept of infinity, highlighting the importance of understanding established mathematical treatments such as Cantor's work on cardinal numbers and Hilbert's paradox of the Grand Hotel. The conversation emphasizes that perceived paradoxes in mathematics are often pseudoparadoxes resulting from incorrect reasoning. Additionally, it clarifies the distinction between the terms "infinite" and "infinity," noting that "infinity" is rarely the correct answer to quantitative questions.

PREREQUISITES
  • Understanding of Cantor's cardinal numbers
  • Familiarity with Hilbert's paradox of the Grand Hotel
  • Basic knowledge of mathematical logic
  • Awareness of terminology related to infinity in mathematics
NEXT STEPS
  • Research Cantor's set theory and its implications on infinity
  • Explore Hilbert's paradox of the Grand Hotel in detail
  • Study mathematical logic to differentiate between paradoxes and pseudoparadoxes
  • Examine the usage of "infinite" versus "infinity" in mathematical contexts
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Mathematicians, educators, students of mathematics, and anyone interested in the philosophical implications and mathematical treatments of infinity.

vishal@physicsforums
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Infinity has been something that has been talked about a lot. A lot of Questions are being posted on this forum and elsewhere about the paradoxes involving infinity.

I want to know if anybody knows some alternate treatment of infinity.
 
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It depends on what you would consider "alternate" view of infinity.

For example, you might consider Cantor's work on cardinal numbers, and Hilbert's paradox of the Grand Hotel (which is not so much of a paradox really) both of which have been written about extensively on wikipedia.
 
You ought to learn the "standard" treatments of the infinite first. There are no (known) paradoxes in mathematics -- only pseudoparadoxes that arise from doing things wrongly.

And incidentally, the word "infinite" is used much more commonly than the word "infinity". e.g. in answer to the question "How many are there?", the answer "infinity" is never correct... although "infinitely many" may be correct.
 

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