Stay at home.
When "home" functions as an adverb, it can modify the verb "stay". There are other examples, such as "go home",but there is no expression:
Go to home.
So I wonder which one is correct.
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People used to think that prepositions had to come before a noun. However, in 1924 a writer called Otto Jespersen realised that prepositions are always prepositions, even if we don't use them with a noun. He also realised that some prepositions never come before nouns.
It took a long time for people to change their thinking. Now, if you look in a modern grammar such as:
... you will see that prepositions are a class of words like nouns, verbs and adjectives. It doesn't matter what kind of words we find them with.
Home in English, is a preposition. There is another word home which is a noun. We can use prepositions and preposition phrases as the complement of the verb BE:
Prepositions can take other preposition phrases as a complement. In other words we often use two prepositions together:
The Original Posters examples
The verb STAY usually takes a locative complement. Usually this complement is a preposition phrase. The word at and home are both prepositions. The sentences:
... are both grammatical.
The preposition to is unusual because we usually need to use it with a noun. So we see:
The word to can't usually come before another preposition:
Notice, though that if we use the noun home instead of the preposition home, then we can use the preposition to
Hope this is helpful!
Now that you mention it, it's an inconsistency in the language. For every other place I can think of, we say "go to" or "stay at/in". "Go to work." "Stay at work." "Go to the store." "Stay at the store." "Go to France." "Stay in France." Etc. No fluent English speaker would say "Go store" or "Stay library".
But with "home", we routinely omit the prepositions. "Stay home" is just as acceptable as "Stay at home", and people almost never say "go to home", it's always "go home".
Hmm, we do say "Go upstairs" and not "Go to upstairs", but I think that's because we're thinking of "upstairs" as a direction rather than a destination.
But note that when used as an adjective, it becomes "stay-at-home", as in, "a stay-at-home mom". No one says, "a stay-home mom".
Idioms and conventions are not always totally logical or consistent. That's what makes learning English such an adventure.
I am an English learner but.. I've been told that 'home' in "I'm home!" is an adverb and my dictionary do say 'home' is used as an adverb. I had been long believing that 'home' is a noun but Collins Dictionary also says it's used as an adverb. I've learned that the grammar is something came after the usage and, for instance, I've learned that 'the hard way' in "I learned it the hard way" is also an adverb. I saw a dictionary in my native tongue has 'the hard way' describing as an adverb. It's an adverb phrase and my grammar book does mention there's something like 'adverb phrase'.
Both are correct. Nevertheless COCAE shows Stay home far too frequently used as compared to Stay at home.
Go to home is okay though very very rare.
One of the examples -
There was a few times I had to get rental skates, go out on the ice, get her off of the ice so that I could go to home and go to work.
To me, this was surprising -
Go home (verb) - return home!
The above mentioned answer answers your concern about you telling someone to stay at home and not go out.
In addition, stay-at-home can also be used as an adjective as J.R. thought worth mentioning here.
Velma works for IBM, and Bruce is a stay-at-home dad. Or: Next year, we plan to start a stay-at-home business.