What is the correct use of the negation of "There to be"?

Question

"There is no man outside the house"
"There is not a man outside the house"

"There was no solution to the problem" "There was not a solution to the problem"

Can I use both of them? Are the sentences equivalent? Which one is more idiomatic?

Answer 1

The two are both acceptable and both in common usage and mean the same thing. Which one you use is purely a matter of personal preference.

Answer 2

They are both correct, but with different emphasis.

"There is no man outside the house"

Lack of a definite article means in the more abstract sense there aren't men outside the house.

"There is not a man outside the house"

When you say "a man", you are being more specific and saying there isn't a person outside.

Context would be necessary to make the distinction clearer. But in the first example perhaps you might be talking about being in a remote, isolated area where people are unlikely to be present. While the latter might refer to someone thinking that they saw a person outside, but then finds that this is not the case.

Answer 3

They are equivalent, as is 'There are zero men outside the house.' The first is good because it is short, but the actual storage in memory is more like the second; Any man (is not outside (of the house)). Every relation is stored with a weighted 'trust'. If this trust is near zero, then the relation becomes a question. If the trust is negative, then the relation is negated ('not' true).