You're merely arguing there that a number is not necessarily an image, because it cannot be converted into one without knowing how. And you'd be right. But the image is still a number, because it's stored as a series of bits, and any series of bits is interpretable as a number.

I asked: "How can an image be a number?", when I should have asked instead: "How can a number be an image?"

To use the verb to be in this scenario, I demand a one-to-one correspondence between numbers and images. If a number y can represent two distinct images x1 and x2, then we can't use "is", we can only use "can be".

Such a strict definition prevents you for using "is" for anything at all! Is that your intention?

To quote a former President, it depends on what your definition of "is" is.

I think everyone here understands that we require information beyond the number itself to get the image. I agree that a more accurate (pedantic) verb is that a number can store or represent an image. That implies that the number alone is not sufficient to get the image.

The thing is that while f can be in theory anything, it will be one of few things in practice. We can say what f is very simply. While knowing f is important, it's also easy to the point of trivial, so some people here are comfortable being less accurate and just saying "a number can be an image."

This reminds me of philosophy of identity discussion me and a friend used to go through. He thought he could fit a Miata in his old-school Suburban - but maybe he'd have to take off the side mirrors. But if he's allowing the side mirrors to be taken off, then how much is too much before it's no longer a Miata?

Indeed often info on which f you need is stored within y. which makes it even easier

Indeed. It seems that for most people here is means can be, while I demand a bit more. Yes, in practice, f will be one of a few mappings, but that does not change the fact that knowledge of f is required. In practice, one merely tries all possible mappings f until one works.

Such lack of precision is only tolerated because computation is fast and cheap. I would love to see people trying all f mappings with the help of an abacus! Let's be thankful that we live in this golden age.

We can go further, actually. We could argue even that (y, f) is not, actually, an image and that's it's just a number and a function. Rather, the image is what's on the screen and only exists when it's displayed.

I'm not trying to continue an argument, but rather just point out that the philosophy of identity can be an elusive thing.

To make things even more fun:

Take an image x, decimate it, and obtain a lower-resolution version of it, which we call z. Are x and z the same image?

Mathematically, no. But when displayed on the screen, then most people would say they are the same. Of course, it depends on the definition of is, but such discussion would be utterly pointless. If we use the same definition, then there's no ambiguity.

But, f is fairly standardized (or rather, there's a short list of standard f's), and bitmaps aren't even hard to understand. Since the isomorphism is both natural and conventional, I would say that in practice it is not accurate to hold f to the same standards as y.