# Can real numbers dimensions exist?

This title may not explain my question right but I could not think of any better short explanation. My question is, if there is a possibility of a structure (or space) with the dimension $$Dim = 3,5$$, $$Dim = 4,8...$$ or any other real numbers value? It's seems pretty obvious that there is no such thing like a $$4,5$$ dimensional sphere but I'm interested in a proof that no such structure can exist. Does a real dimensional space make any physical sense? Thanks for your help.

• Depends on how you define the word “dimension”. What do you have in mind? – knzhou Apr 11 '19 at 9:58
• I think of dimensions, like the euklidien space. – gamma Apr 11 '19 at 11:11
• What you're looking for are fractal dimensions. Take a look at this video for a nice introduction youtube.com/watch?v=gB9n2gHsHN4 – Halbeard Apr 11 '19 at 11:20