A thing is missing from this submission. This thing is a common sight, and this submission’s grammar and word options may function as hints to its solution, which is a trinity of words.

I fly by like a bird, yet I have no wings. You kill me, yet I remain living. Not physical, not visible, yet I can be checked. But when you say I swing, my speed never changed.

I include much, but much is not me. I am considered to be everything.

My maker does not keep me, my buyer does not use me, and my user does not see me. What am I?

I'm by design a sign of turbulence, though often symmetrical. I raise your arms in patterns, yet am found in the mathematical.