Alternate Treatment of Infinity

  • Thread starter Thread starter vishal@physicsforums
  • Start date Start date
  • Tags Tags
    Infinity Treatment
AI Thread Summary
Infinity is a widely discussed topic, particularly concerning its paradoxes and alternate treatments. Notable concepts include Cantor's work on cardinal numbers and Hilbert's Grand Hotel, which challenge traditional views on infinity. Understanding standard treatments of infinity is essential before exploring alternative perspectives. The distinction between "infinite" and "infinity" is important, as "infinity" is often misused in mathematical contexts. Ultimately, there are no true paradoxes in mathematics, only misconceptions that arise from incorrect applications.
vishal@physicsforums
Messages
2
Reaction score
0
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.
 
Mathematics news on Phys.org
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.
 
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top