на Украинеis correct Russian,
die E-Mailis correct German, and in English do use the serial comma consistently. (Though certain authorities use other variants for economical or political reasons, the above variants are standard in the wide sense of the word. We use languages as means of communication; we do not try to change languages.)
Now one thing I have to tell you. In this particular show you have to be armed to enforce your authority. But you're not to use your weapon under any circumstances. Under any circumstances. Is that quite clear?(Ernest Hemingway, The Fifth Column.)
Some details on MD5. (The same goes for other hash functions, say, SHA1.)
Let's assume that you have never typed in a particular large number, say, 89434823561. And you have never seen it so far. And no one you know has ever seen this number. Neither have your colleagues, though you don't speak to them. On this empirical basis, you declare this number nonexistent for all practical purposes. Encountering this number in the future is less likely than the probability of finding oneself with those two sweet blond ladies you always wanted at your home in a horizontal position simultaneously. Since instead of the ladies, you have been enduring the society of your wife for quite a while, well, you decide to use the value 89434823561 as an error value when, say, returning the file size.
Is it clever? Of course NO. There is absolutely nothing which precludes the next large file you see to have size exactly 89434823561. There is absolutely nothing which precludes the next two large files you see to have this size. As the time goes by, files get larger, so 89 GB files may be the norm in a decade or so. (Cute ladies will stay away, though. Sigh.)
However, this is exactly what happens when you are using hash functions to verify the equality between the buffers of your application or between your files, just with a more complicated mathematical formulation and at a slightly different scale.
So don't use hash functions to test data equality. Naturally, testing data inequality (if hash(𝑥) ≠ hash(𝑦), then 𝑥 ≠ 𝑦) is still fine.
Yes. Up to isomorphism.
The Theory of Gears.So he goes. The speaker stands up and begins,
The theory of gears with a real number of teeth is well known ….
G, H. Hardy. (J. E. Littlewood, A Mathematician's Miscellany.)
Up and Down The Temporal Wayby Howard Barringer starts with
A formal specification of a multiple-life system is constructed.Such a sparkling and lively Up-and-Down is not too bad for a paper on multiple lifts. Though this error occurred during optical character recognition, Oxford University Press refused to correct the typo.
I'd like to have half a liter of beer.The second says:
I'd like to have one fourth of a liter.The third one:
I'd like to have one eighth.The barman says:
Hey, stop that. Know your limits: you'll get one liter for all.