TST: check freq on series.index in assert_series_equal
Before long we'll roll that check into assert_index_equal
thanks This is a backwards incompatible change, that will break downstream projects' tests. Only there tests of course, not actual users, but still potentially annoying (this started breaking the arrow tests we run against pandas master). 

Are we sure we actually want to test the `freq` by default? It could also be an opt-in keyword, that you can call for those tests where you explicitly want to test this.  I don't have a strong opinion here, but do we think that these should compare equal?

```python
In [14]: a = pd.DatetimeIndex(['2000'])

In [15]: b = pd.DatetimeIndex(['2000'], freq='D')
```

They have the same values but different `freq`.

In general, I think our test functions should be strict by default with keywords allow looser comparisons. So I'm probably OK with those not asserting equal. It maybe depends a bit on how you see the "freq". Is it an attribute that actually changes how we interpret the data, or is it rather like a cached property for which we do more effort to preserve it (since it can expensive to infer each time we need it) ?

In the first case, it certainly makes sense to check it by default, but in the second interpretation, not so much IMO.

(now, which interpretation is most correct, I don't directly know, I am not that familiar with how it is used across pandas) Yeah, I think you've accurately summarized the situation. I think, though, that whether `freq` is just a cached attribute or an intrinsic property of the Index is a bit fuzzy.

If we think it's just a cached attribute then I'm happy to exclude it from the assertions (by default).

If it's an intrinsic property, then I think the default should be to raise if it doesn't match. @jbrockmendel @jreback some response here? my plan is to add a `check_freq` keyword that defaults to True.  Moving forward with this is blocked by #33836.

 And why do you think the default should be True? (not that the other PR shouldn't move forward, but why does factorize block adding `check_freq` in assert_index_equal?) > (not that the other PR shouldn't move forward, but why does factorize block adding check_freq in assert_index_equal?)

factorize doesnt block per se, but im trying to keep only one freq-checking-related PR active at a time.

> And why do you think the default should be True?

Because failing to check freq allows for bugs to go unsurfed.  e.g. the author of [this](https://github.com/pandas-dev/pandas/pull/33836/files#diff-e5dda746a1d5340bb5bbb45b4ae5b47aL84) test  apparently thought that freq was being checked when it isnt Well, when you know you want to preserve the freq and test this, you can pass the keyword when it is not the default. 

 > Well, when you know you want to preserve the freq and test this, you can pass the keyword when it is not the default.

checking frequency should be the default, I totally agree with @jbrockmendel if we care about freq then we need to always check, when its None, that's fine as well, but if something is not the default rarely to authors or reviewers catch this (and has been a large source of bugs).

relying on 'manual' things is big -1 always. > if we care about freq then we need to always check

But often we *don't* care about freq. See the many cases in this PR that removed the freq before testing. 

Therefore I asked the question about whether freq is more like a fancy cached property or not? (https://github.com/pandas-dev/pandas/pull/33815#issuecomment-623522559 and to repeat from there, I don't necessarily know the answer, but you also didn't reply to that)

And to repeat, this is a backwards incompatible change, that will break the tests of almost any downstream project that uses timeseries. 
And in this PR it is actually being solved with a private API.