In an earlier post, I entertained the idea that a number (would it be a number? Well, it would be something) $Φ$ existed such that the interval $[0,Φ]$ would include only $0$ and $Φ$.
In other words, $Φ$ such that $0<Φ< ℝ+$.
This pretty clearly does not make sense. But today I was thinking about this and how it compares to $i$, another number that does not seem sensible at first glance.
My question is: how exactly does a term like $i$ find general approval and integration into standard mathematics while other 'imaginary' concepts such as the $Φ$ I speculated on above not?
(just a thought experiment past this point, I'm making this up as I go)
Just like $i$ can find practical usage in mathematics and physics, can't ideas/numbers like the $Φ$ I described be able to find usage as well; for instance, could a number such as $Φ$ be used a useful shorthand in epsilon-delta problems?