(adsbygoogle = window.adsbygoogle || []).push({}); Functions that "introduce" new degrees of freedom?

OK, I realize this is a wacky question, so forgive me!

BUTI was thinking about it the other day, and suppose I had a 2 dimensional space [tex]\Bbb{R}^{2}[/tex]. Is there any function that generally exists as: [tex]f: \Bbb{R}^{n} \rightarrow \Bbb{R}^{n+1}[/tex]? So in my scenario, it would be [tex]f: \Bbb{R}^{2} \rightarrow \Bbb{R}^{3}[/tex]...

Would this still be part of set theory or has this entered some other field?

Now, an additional question, I am a programmer and I know I can code "IF p=x THEN add a new dimension" or something of the sort. Is there anything in math that has a counterpart to this? Boolean functions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Functions that introduce new degrees of freedom?

**Physics Forums | Science Articles, Homework Help, Discussion**