There is only one way to understand the difference between lenses used on different formats. Look at images. All this messing around with formulas does nothing. Look at the images and you realize 50mm FF is not the same as 35mm APS-c. It may be equivalent in FoV and DoF with proper adjustments, but in the end, it's just not.
I shoot most of my stationary subjects at every f-stop form ƒ2.8 to ƒ11 and then pick the one I like most. You have to do the same with an equivalent lens in FF or APS-c. And I can't believe you guys don't know your camera systems well enough to see a shot and "go in your head 50mm FF or, 70mm APS-c" That info should come to mind as soon as you see the scene with the camera in your hand. Honestly, if you're doing calculations in your head, I suspect you're missing out. Many times the issue is "what lens do I want to use for this picture" and it has nothing to do with format. There are times when you look at a scene and say "21 ltd." and that's what you want to use, even if you have to walk forward or back, because that lens renders the way you want that image to look. And no the 31 on FF isn't the same. That's the thing I understand least about all this emphasis on formulas and equivalence. I don't think focal length. I think how do I use the lens I think best suits the scene I have in front of me. Working out focal lengths is probably the last thing going through my mind. Accept for the crucial decision on how long a lens I want and how much I want to narrow or expand my FoV, behind my subject.
Quote: it's got nothing to do with pushing the film.
Of the stupid things you've said, that pretty much takes the cake. But here let me explain it to you again, even though you'll just claim I'm wrong....
When you push film you intentionally underexpose and then over develop. It's a basic technique that was taught in the first year of every photography class, ever. It essentially increases your ISO, and contrast, but also increases your grain size.
I do the same thing in digital, by exposing to the left which is in essence an underexposure, I then use the levels control to make full use of the limited dynamic range I've captured, effectively increasing my ISO, and because of the structure of digital files, my contrast, but also increase my noise, very much like film.
But hey dude, don't bother telling me I don't know what i'm talking about again, I know what you think of me, and so does everyone else. This is for anyone starting out who might be confused by the amount you think you know, that you know nothing about.