Why is the negation of: Atleast one hole contains atleast n+1 pigeons where n is a natural number
There are less than n+1 pigeons per hole?
Wouldn't it be: There are less than one hole that contains less than n+1 pigeons?
Wouldn't the negation of there exists a hole that contains atleast n+1 pigeons yield
all holes contain less than n+1 pigeons?
Why is the existential quantifier assumed for the phrase: "Atleast one hole" in the first part of the sentence but not for the "atleast n+1 pigeons"?