- #1
Loud Red
- 4
- 0
Functions that "introduce" new degrees of freedom?
OK, I realize this is a wacky question, so forgive me!
BUT I 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?
OK, I realize this is a wacky question, so forgive me!
BUT I 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?