So, this is a bit of a dumb question but I'm trying to understand why it's called a "partially ordered set" and not just an "ordered set," so according to old, handy [Wikipedia/Partially ordered set](https://en.wikipedia.org/wiki/Partially_ordered_set):

> the word "partial" in the names "partial order" or "partially ordered set" is used as an indication that not every pair of elements need be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable.

So, one example of this might be the set {\\(a, b, c, 1, 2, 3\\)} where the first subset {\\(a, b, c\\)} is ordered alphabetically ascending and the second subset {\\(1, 2, 3\\)} is ordered numerically ascending? If that's the case then does that mean since the first subset can't be compared to the second subset, then set {\\(a, b, c, 1, 2, 3\\)} is equivalent to {\\(1, 2, 3, a, b, c\\)}?

> the word "partial" in the names "partial order" or "partially ordered set" is used as an indication that not every pair of elements need be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable.

So, one example of this might be the set {\\(a, b, c, 1, 2, 3\\)} where the first subset {\\(a, b, c\\)} is ordered alphabetically ascending and the second subset {\\(1, 2, 3\\)} is ordered numerically ascending? If that's the case then does that mean since the first subset can't be compared to the second subset, then set {\\(a, b, c, 1, 2, 3\\)} is equivalent to {\\(1, 2, 3, a, b, c\\)}?