Complex is used to refer to the level of components in a system. If a problem is complex, it means that it has many components. Complexity does not evoke difficulty.
On the other hand, complicated refers to a high level of difficulty. If a problem is complicated, there might be or might not be many parts but it will certainly take a lot of hard work to solve.
Cardinalis means "that upon which a door hinges, pivotal" in Latin, from cardo, "hinge, pivot". From this it acquired its secondary meaning, "important, principal", which it still has in English (e.g. a cardinal sin). Its third meaning is derived from this: a cardinal number is a "principal" number, i.e. one that simply says how many objects there are.
That'll be one pound.
Two billion people might die.
Ordinalis means "in order of succession, of an order". It comes from ordo, "order, rank". An ordinal number is an adjective that denotes what place an object has in a certain order. The names of the ordinal numbers are usually derived from the cardinal numbers by adding -th.
That is my second victory.
This is the tenth time she's dumped me.
While a cardinal number refers to several objects ("three apples"), an ordinal number refers to only one of those ("the third apple"). An ordinal number is hence dependent on the notion of a cardinal number: there can't be a third apple unless there are at least three apples. By contrast, there can be three apples without one being the third, if they are just not arranged in any particular order.
The Romans used these terms the same way. They also had distributive numbers, which indicated "every third apple", or apples "in triads", "three each".
Best Answer
The two phrases often have similar meanings and uses, but in many cases are not interchangable. For example, in “She made the cake from scratch”, which means she made the cake from separate ingredients rather than from a mix, from the ground up won't substitute properly for from scratch. Another instance where that substitution won't work is “The cave grew its stalactites from scratch”.
Generally, from scratch has two senses: “From the beginning; starting with no advantage or prior preparation” and “From basic materials or raw ingredients” (wiktionary). From the ground up has one sense: “From the beginning; starting with the basics, foundation, or fundamentals” (wiktionary). For example, if you are talking about developing a theory from first principles, from the ground up is more suitable than from scratch due to its foundation or fundamentals connotation. If you want to emphasize building something from basic components, from scratch may be better.