I don't think anyone is saying that it is saying the same thing.

Saying that x² = 16 merely imposes constraints on the values that x can take on and have this equation satisfied. If it takes on either x = 4 or x = -4, then the equation will be satisfied. If it takes on other values, the equation won't be satisfied.

Alright thanks I will make sure to work and practice on introductory algebra text !

thank you very much

 

Doesn't really matter if it "feels wrong". When discussing infinite sets, lots of things don't "feel right" to our everyday sense of propriety.

But when it comes to the language we use, of course it matters. The word equinumerous implies "an equal number of things", which is a fine adjective for things that can actually be counted, whether finite or infinite.

http://mathworld.wolfram.com/Equinumerous.html

However, it is confusing at best -- and nonsensical at worst -- to call two uncountable sets equinumerous. For instance, there is a bijection between every point in the unit cube in ℝ×ℝ×ℝ and a sliver on the real line, say [0, 0.01]. Does that mean that both sets have the same number of things? No, of course not; the notion of counting is undefined on these sets. The proper terminology is to say that they have the same cardinality, which is not a synonym for size. In contrast, the Lebesgue measure does correspond to a general notion of size, and it tells us that the volume of the cube is 1, while the length of the interval is 0.01. In other words, though their cardinality is the same, their sizes are certainly different (just as we'd expect). Calling them equinumerous is grossly misleading.

For countably infinite sets, calling them equinumerous is tolerable, though wholly unnecessary when we have such a fine word in cardinality, which applies to any and all sets without the conceptual overloading that "equinumerous" requires.

Anyway, that's my language matters argument for the day.