You are not talking about a specific mirror, just the general idea of "mirror." If you had a specific mirror, it would be different: "Tengo un espejo viejo." But I never really know for sure!! I have asked teachers, in Mexico and Argentina, about "el queso" or "queso" in a sentence and received a shoulder shrug and a look of "whatever!" ;)
In a different discussion about "No tengo secadora" a native Spanish speaker explained that you don't use "una" there because it would imply that you have more than one dryer - two or three maybe. So now I think of this kind of negative-having sentence as "I have no (not even one) sofa/dryer/mirror or whatever" Hope that helps.
the article shouldn't be used even though it's used in English, Frequently after forms of tener ("to have"), comprar ("to buy"), llevar ("to wear") and some other verbs when generically referring to things that people would normally have or use one at a time: No tengo coche. I don't have a car. Lleva camisa. He is wearing a shirt. Vamos a comprar casa. We're going to buy a house. ¿Tiene madre? Does he have a mother?
@deadinibiza - re: Who talks like that in english??
Hola. This is an issue with Duo that comes up a lot. As native English speakers we use our own empirical knowledge of phrases as a guide for what sounds right to our ears.
However, when we get great posts from users like itsmesd and EugeniaAlb, it becomes clear that Spanish can convey subtle nuances by using grammatical structures that are not commly used in the minds of many English speaks from various regions around the world.
It sounds very plausible that the expression "I don't have a (fill in the blank)" in English is used around the entire English speaking world, to mean "I don't have even a single (fill in the blank)."
However, it also sounds equally plausible that claiming, "I don't have (fill in the blank)" in Spanish leaves open the possibility that more than one of the item could be possessed by the speaker.
But the claim "I have NO (fill in the blank)" seems to close that ambiguity by making it clear, no number of them is possessed by the speaker.
Although the sentence structure "I have NO (whatever)" may sound incorrect to different English speakers from various regions, it is grammatically correct and preserves more of the nuance of the root sentence.
In some cases it's important to understand the culture, situation and semantics behind the root language sentence and take that into account when crafting a translation in a target language that may not possess the same drivers.
Even at the expense of creating a translation sentence that you would commonly say yourself.
In English, you need the article if it's a singular countable noun. So, "I do not have a mirror.", or "I do not have the mirror." when the definite article is appropriate, but "I do not have air." (uncountable) and "I do not have mirrors" (plural) or "I do not have the mirrors" (plural, definite).
Although I believe "I have not got a mirror" is improper grammar. "I haven't got a mirror" translates out as "I have not got a mirror," as "haven't" is the contraction of "have not." Once we extend it to the full words we can see how it sounds wrong. Commonly used? Most definitely, (even by me! :) ) but proper? Not really. Just a note. :)