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I'm a data scientist, and it relieved me no end that I got this one right: http://i.imgur.com/V5oJ4i4.png http://i.imgur.com/V5oJ4i4.png I would have had second
by dude_abides 11y ago
I'm a data scientist, and it relieved me no end that I got this one right: http://i.imgur.com/V5oJ4i4.png http://i.imgur.com/V5oJ4i4.png I would have had second thoughts about my career choice if I got this wrong :)
The correct approach for any data modeling problem is to think in terms of entropy. Each subsequent approach should minimize entropy, until you reach diminishing returns.
- taigeair 11y agoI got so many nos. I can't believe that "Remarkably, 77 percent of people who have played this game so far have guessed the answer without first hearing a single no." That's crazy.
- Sadgrinner 11y agoIsn't your answer technically wrong, though? The sequence is not monotonically increasing. It's strictly increasing. If you test [1, 1, 2] or [1, 1, 1] or [1, 2, 2], you'll get "No" answers even though those sequences are monotonically increasing.
- thaumasiotes 11y agoNot so. http://mathworld.wolfram.com/MonotoneIncreasing.html http://mathworld.wolfram.com/MonotoneIncreasing.html
- ddlatham 11y agoSo. http://mathworld.wolfram.com/MonotonicFunction.html http://mathworld.wolfram.com/MonotonicFunction.html https://en.wikipedia.org/wiki/Monotonic_function https://en.wikipedia.org/wiki/Monotonic_function
- thaumasiotes 11y agoYou think the definition of "monotonic function" is more relevant to the meaning of "monotonically increasing sequence" than the definition of "monotone increasing" is? [1,1,2], [1,1,1], and [1,2,2] are not monotone increasing. They're also not monotonic functions.
- Sadgrinner 11y agoIn all seriousness, the definition of monotonically increasing that I was taught is the same as exists in wikipedia: "A function is called monotonically increasing (also increasing or non-decreasing), if for all x and y such that x <= y one has f(x) <= f(y). https://en.wikipedia.org/wiki/Monotonic_function#/media/File:Monotonicity_example1.png https://en.wikipedia.org/wiki/Monotonic_function#/media/File... This definition allows for 'flatness' in a graph, since the derivative does not change sign. Or, from http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L8.html http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/... : A sequence f(n) is monotonic increasing if f(n+1) ≥ f(n) for all n ∈ N. The sequence is *strictly* monotonic increasing if we have > in the definition instead of ≥.
- thaumasiotes 11y agoYou can draw that contrast (increasing vs strictly increasing), but what I was taught was to contrast increasing functions/sequences with nondecreasing functions/sequences. A book or paper will make it clear what they mean by "increasing" by using the definition. There, it doesn't matter at all -- they could just as easily coin new words, since they immediately give the full definition. But the people hanging around this thread, telling people who are using a very common definition of "monotonically increasing" that (in paraphrase) "I hate to be pedantic, but you've made a mistake, in that I would have phrased that differently" have failed to contribute anything or to be pedantically correct. There's no case to be made that, if I say a "monotonically increasing sequence" must be increasing rather than nondecreasing, I've made a terminological mistake. This is a term with different definitions in different treatments.
- ddlatham 11y agoThanks for your perspective. It's interesting that there appears to be ambiguity in the terms and a diversity in what is being taught.