# Why isn't \`Vector{\<:Float64}\` reduced to \`Vector{Float64}\`?

**URL:** <https://discourse.julialang.org/t/why-isnt-vector-float64-reduced-to-vector-float64/117555>\
**Category:** General Usage\
**Tags:** type, parametric-types\
**Created:** [July 28, 2024, 12:49am UTC](https://discourse.julialang.org/t/why-isnt-vector-float64-reduced-to-vector-float64/117555 "2024-07-28T00:49:44Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [July 28, 2024, 12:54am UTC](https://discourse.julialang.org/t/why-isnt-vector-float64-reduced-to-vector-float64/117555/2 "2024-07-28T00:54:19Z")

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This is in the [Julia FAQ](https://docs.julialang.org/en/v1/manual/faq/#Troubleshooting-%22method-not-matched%22:-parametric-type-invariance-and-MethodErrors). There are many discussions that try to help explain this. See e.g.

- [Problem with Complex{Rationals} - #7 by stevengj](https://discourse.julialang.org/t/problem-with-complex-rationals/9474/7)
- [Why [1, 2, 3] is not a Vector{Number}? - #19 by stevengj](https://discourse.julialang.org/t/why-1-2-3-is-not-a-vector-number/52645/19)
- [Why [1, 2, 3] is not a Vector{Number}? - #28 by StefanKarpinski](https://discourse.julialang.org/t/why-1-2-3-is-not-a-vector-number/52645/28)

~~I guess you are asking specifically about `Vector{<:Float64}`. Realize that `Vector{<:T}` for _any_ type `T` is a _set_ of types: `Vector` types for any subtype of `T`. Now, I guess your point is that, since `Float64` is concrete, it has exactly one subtype `Float64`, so `Vector{<:Float64}` is a **set containing only one element** , `Vector{Float64}`. Still, in mathematics we generally don’t equate a set of a single element with that element: \{x\} \ne x.~~ As noted by @nsajko below, the bottom type `Union{}` is a subtype of `Float64`, so `Vector{Union{}} <: Vector{<:Float64}`.

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