1. He is a very kind boy.

2. A fox is a cunning animal.

(Is the meaning of 'a' before 'very' the same as the meaning of 'a' before 'cunning'?)

3. Once there lived an old man.
4. Once there lived one old man.
(In this sentence does 'an' mean 'one'? Are both the same?)

1 and 2 -- Yes, "a" indicates there's one.

3 and 4 are about the same, but 3 is smoother.

The "a" is a modifier of the nouns - boy and animal...

"an" means "one".

"an" is used instead of "a" when the following word starts with a vowel, such as "old man"

It might help a little more to distinguish between the use of "a" and "the."

It is a correct answer.
It is the correct answer.

In this case, "a" infers it is one of other correct answers. In contrast, "the" indicates that it is the only correct answer.

I hope this helps a little more. Thanks for asking.

1. In the sentence "He is a very kind boy," the word "a" is an indefinite article used before the adjective "very" to indicate that the noun "boy" is being referred to in a non-specific way. It suggests that there are other kind boys in general, and the boy being mentioned is just one example among them.

2. Similarly, in the sentence "A fox is a cunning animal," the word "a" is also an indefinite article used before the adjective "cunning." It indicates that the noun "animal" is being referred to in a non-specific way, suggesting that there are other cunning animals. In this case, "a" can also be interpreted as "one" if we consider the adjective "cunning" to be more specific to a particular fox.

3. In the sentence "Once there lived an old man," the word "an" is an indefinite article used before the adjective "old" to indicate that the noun "man" is being referred to in a non-specific way. It suggests that there are other old men in general, and the old man being mentioned is just one example among them.

4. In the sentence "Once there lived one old man," the word "one" is not used as an indefinite article but as a cardinal number. "One" is used here to specify that there is only a single old man being referred to, rather than multiple old men. It emphasizes singularity.

So, in this context, "an" and "one" are not exactly the same. "An" is an indefinite article, while "one" is a cardinal number used to indicate singularity.