It sounds the lecturer is saying

we've explored the relationship between functions and their gradient

gradient's plural should be gradients.

So, the sentence should be ... between functions and their gradients, am I right?

Here is another proof

  • But what if the functions do have a relationship with a single gradient? You are making an assumption that may or may not be true. Both these apples come from a grocery store and these apples come from grocery stores are fine. There's nothing necessarily wrong with the grammar. – Jason Bassford Jul 15 '19 at 13:19
  • I find it somewhat curious that he used the term gradient at all to talk about a single variable derivative, but I think that may be because he is going to skip over all the theory. Are you taking this for credit? – Ron Jensen - We are all Monica Jul 15 '19 at 16:48

Looking at your video, it does seem that the lecturer is talking about the relationship between functions and their respective gradients. So maybe he should have said "functions and their gradients", or used the singular form in its "generalizing" capacity:

"we've explored the relationship between a function and its gradient"

But this is such a common grammar error that it doesn't even sound strange to me. I think most native speakers of English would not even notice that there was anything wrong with his phrasing unless you challenged them to find the mistake in that specific sentence.

Since the professor's topic is Math and not English Grammar, I think we should excuse him this time. (But yes, you are right.)

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