Describing a Cyclic Space: 0 = 1

In summary, a cyclic space is a space where the endpoints are equal (0=1). It can also be referred to as a cyclic dimension, but this terminology may not be widely used. Terms used to describe this type of space include "cyclic interval" or "cyclic field" (although it is not technically a field). This type of space is often represented as R/Z or the unit circle in the complex plane with t \to \exp(2\pi t).
  • #1
yetar
54
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.
 
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  • #2
Oops, perhaps it should be called cyclic field.
But can I also call it cyclic space or cyclic dimension?
 
  • #3
You're talking about R/Z. The reals modulo the integers. It can be identified with the unit circle in the complex plane by [itex]t \to \exp(2\pi t)[/itex].

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.
 
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FAQ: Describing a Cyclic Space: 0 = 1

What is a cyclic space?

A cyclic space is a mathematical concept that describes a repeating pattern or cycle in a given space. It can refer to physical phenomena, such as the orbit of a planet, or abstract concepts, such as a repeating sequence of numbers.

How does 0 = 1 in a cyclic space?

In a cyclic space, 0 = 1 means that the starting point and the ending point of a cycle are the same. This can be visualized as a loop or circle, where the beginning and end are connected.

What is the significance of 0 = 1 in a cyclic space?

In a cyclic space, 0 = 1 represents the concept of infinity and the idea that the cycle will continue indefinitely. It also highlights the interconnectedness and symmetry of the cyclic space.

Can a cyclic space have more than one cycle?

Yes, a cyclic space can have multiple cycles within it. These cycles can overlap, intersect, or be completely separate from each other.

How is a cyclic space studied and applied in science?

Cyclic spaces are studied and applied in various fields of science, such as physics, chemistry, and biology. They can help us understand and predict natural phenomena, model complex systems, and design experiments. Cyclic spaces are also used in computer science and engineering to develop algorithms and solve problems.

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