# Why the dimension of V1 = ℤ₂Space(0=\>3,1=\>2) is 5?

**URL:** <https://discourse.julialang.org/t/why-the-dimension-of-v1-space-0-3-1-2-is-5/59960>\
**Category:** Numerics\
**Created:** [April 25, 2021, 12:29am UTC](https://discourse.julialang.org/t/why-the-dimension-of-v1-space-0-3-1-2-is-5/59960 "2021-04-25T00:29:48Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![Nellatur](https://avatars.discourse-cdn.com/v4/letter/n/76d3ee/32.png) [@Nellatur](https://discourse.julialang.org/u/Nellatur)\
**Post date:** [April 25, 2021, 12:29am UTC](https://discourse.julialang.org/t/why-the-dimension-of-v1-space-0-3-1-2-is-5/59960/1 "2021-04-25T00:29:48Z")

</div>

I am not sure if this question would belong to mathematics or more suitable for mathematics stackexchange. It comes from  
[https://jutho.github.io/TensorKit.jl/stable/man/tutorial/#Symmetries](https://jutho.github.io/TensorKit.jl/stable/man/tutorial/#Symmetries)

```julia
julia> V1 = ℤ₂Space(0=>3,1=>2)
Rep[ℤ₂](0=>3, 1=>2)

julia> dim(V1)
5

```

I think Z2 is cyclic group, [Cyclic group:Z2 - Groupprops](https://groupprops.subwiki.org/wiki/Cyclic_group:Z2), but why the dimension is 5? In some representation?