Hi everyone I searched a bit and couldn't find anything quite specifically for what i'm looking for. Am curious to know what is the best way to symbolically write or convey the idea of 'I'm rewriting this as' or 'lets look at it this way'.
The logically equivalent symbol $ \equiv $ comes closest I think but is it appropriate to use it in cases like: $$ 2a \leq 2^n \equiv a+a \leq 2 \cdot 2^{n-1}$$
In this case is it just preferable to use brackets if I want to expand out the inequality like this ie: $$ (2a \leq 2^n ) = (a + a \leq 2 \cdot 2^{n-1}) $$
just doesn't really seem right. And while = typically works I have found in some cases it can cause a bit of ambiguity I prefer to avoid especially when starting out on working out problems. Another example would be something like:
$$ (g \circ f) (x) \equiv g(f(x)) $$
Again here equals doesn't seem quite right but but neither does logically equivalent as there's no truth value involved - I'm just trying to frame the meaning different and remind myself or reader how we're going to approach it.
Hopefully question makes sense its just I haven't found quite explaining this and am just wondering if there is a standard or common way of doing this. I just like the idea of having something concise that means 'can be rewritten as' etc. Thanks.