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Sorry if this is a duplicate / not something allowed in here, I do not use the math section often.

I am looking for a word to describe something that cannot be calculated "backwards", once it is calculated "forwards". Maybe it is a relation of some sort?

One example might be found in cryptography I think, where, for example, when you calculate a compressed hash out of something, you cannot really calculate the original information back from the hash. What is that phenomenon called? Are there different words to describe something like that?

Swiffy
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    Possibly "one-way function"? – Minus One-Twelfth Feb 21 '19 at 07:39
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    @MinusOne-Twelfth I think one-way functions could be some of the instances of this? Is there a more general definition / term to describe this "one-wayism"? I mean if I have a rock and I grind it to sand, that relationship between the sand and the original rock would also be pretty one-way, as it would be quite impossible to construct the original rock back from the sand. Would you describe this example simply as an "example of one-way relationship" or something else? – Swiffy Feb 21 '19 at 07:47
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    The first thing that came to mind was the notion of a function which is not injective. If a function is injective, then unequal inputs lead to unequal outputs, i.e. $x\neq y \implies f(x)\neq f(y)$. This is also equivalently stated as $f(x)=f(y) \implies x=y$. If a function is not injective, you cannot necessarily have $f^{-1}(f(x)) = x$ or $f(f^{-1}(x))=x$, i.e. you cannot retrieve the input despite knowing the output and the function. An example is $f(x) = x^2$. If I tell you $f(x) = 4$, you can't tell me for sure whether $x$ was $2$ or $-2$. – PrincessEev Feb 21 '19 at 07:49
  • Isn't it unrealistic to expect one definition that includes the "one-way functions" and the rock and sand example? The first example already carries a nice definition and the second can probably be described by a physicist in terms of entropy. I don't see a need for one formal definition to include all these phenomena in one go. – Mathematician 42 Feb 21 '19 at 07:52
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    Perhaps you looking for "non-reversible", which describes an operation which cannot be done in the opposite direction in a one-to-one fashion. The opposite will, of course, be that the operation is "reversible". – John Omielan Feb 21 '19 at 07:55
  • @EeveeTrainer Aha! That's a good one and pretty familiar to me, especially in the context of functions. So I guess I could call things that have one-way relationships as things which relationship is not injective? Then again, why wouldn't I just call not injective relationships as one-way relationships... – Swiffy Feb 21 '19 at 07:55
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    @JohnOmielan Yes! That is definitely the word I was looking for! It was completely lost on me, I am not a native english speaker either so no wonder. :) I would mark that one as an accepted answer, if you post it. – Swiffy Feb 21 '19 at 07:57
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    I've done as you requested, and am glad I could be of help. – John Omielan Feb 21 '19 at 07:58

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Perhaps you're looking for "non-reversible", which describes an operation which cannot be done in the reverse direction in a one-to-one fashion. The opposite will, of course, be that the operation is "reversible".

John Omielan
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