Describing a Cyclic Space: 0 = 1

  • Thread starter Thread starter yetar
  • Start date Start date
  • Tags Tags
    Matter Terms
AI Thread Summary
A cyclic space can be described as the interval [0, 1] where 0 equals 1, often represented by R/Z, which corresponds to the unit circle in the complex plane. The term "cyclic dimension" is not commonly used, and referring to it as a cyclic field is incorrect due to the lack of a multiplicative identity. While the concept of cyclic space may not be widely accepted, it is important to clarify terminology in mathematical discussions. The identification with the unit circle emphasizes its cyclical nature. Ultimately, precise language is crucial for effective communication in mathematics.
yetar
Messages
53
Reaction score
0
If I have a cyclic space, [0, 1] where 0 is equal to 1.
Can I also call it a cyclic dimension?
What are the terms of describing this cyclic interval/space etc?

Thank you.
 
Mathematics news on Phys.org
Oops, perhaps it should be called cyclic field.
But can I also call it cyclic space or cyclic dimension?
 
You're talking about R/Z. The reals modulo the integers. It can be identified with the unit circle in the complex plane by t \to \exp(2\pi t).

If you call it a cyclic space, or dimension, I imagine you'd be alone in doing so. It is not a field, since it doesn't have a multiplicative identity.
 
Last edited:

Thread 'Fermat's Last Theorem'

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...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

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...
View full post »
Thread 'Imaginary Pythagorus'

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...
View full post »

Similar threads

Simulation of Cyclic Loading in Tensile Test
Replies
14
Views
2K
MHB Couple of hard trig questions....
Replies
1
Views
2K
Internal energy won't add up to 0 in cyclic process
Replies
1
Views
883
B Is Infinity Cyclical or Linear?
Replies
35
Views
4K
Insights Why Vector Spaces Explain The World: A Historical Perspective
Replies
0
Views
7K
MHB DFT for convolution like operation.
Replies
2
Views
2K
Glucose structure and insulin resistance
Replies
3
Views
3K
Find Yield displacement and Yield strength of steel under cyclic load
Replies
5
Views
2K
I Difficulty with function dependencies f(u,x)
Replies
7
Views
2K
B Roger Penrose model of the rebirthing universe
Replies
16
Views
3K

Hot Threads

Recent Insights

Back
Top