4 ms·

> δ is also typical (though not "standard") for "small difference" No, that's epsilon. In this area, delta is usually a probability. Epsilon-delta statements a

• ndriscoll 3y ago
  Epsilon and delta both often represent small changes. Epsilon typically represents an "error" size. Very often, when they appear together, delta is a small change in the input of something, and epsilon is the corresponding change in the output. So e.g. in lots of analysis proofs, you want an output error less than epsilon, and must figure out the required bound on delta to achieve that. Maybe there's a way in which your sense is an example of the above sense, but it's too early for me to think about that. In any case, in your sense, typically delta is implicitly meant to be thought of as small. Anyway, point is mathematics is a language. Like all languages, it's inseparable from its culture. The symbols often carry conventional meaning and aren't purely formal/arbitrary. This helps the speakers of that language communicate more efficiently, but it means outsiders need to learn the culture too in order to properly understand "native" level speakers. And like other languages, many parts of written mathematics just don't translate correctly to another language.
  • ot 3y ago
    > Anyway, point is mathematics is a language. Yes, and like any language there is context-dependence. In calculus you're right, epsilon and delta are usually small variations (for example in the definition of a limit). In randomized algorithms, if you say epsilon-delta anybody will immediately associate delta with an error probability.