Definition
Existence
Existence means that at least one object or value satisfies all the stated conditions.
What it means
To prove existence, you only need to show that something works. Sometimes you can point to one example; sometimes reasoning proves that an example must be there even before you find it.
Remember it
One working example is enough to unlock “there exists.”
Example
The fraction 3/4 is greater than 1/2 and less than 1. Because 3/4 meets both conditions, it is a witness proving that a fraction between 1/2 and 1 exists.
Watch for
Existence means at least one solution, not exactly one. More solutions may also satisfy the conditions.
Common mix-up
“It might exist” is a possibility claim. An existence proof supplies a witness or reasoning that guarantees at least one.
Exact meaning
An existence claim says that at least one object or value satisfies all stated conditions. It can be proved by giving a valid example, called a witness, or by an argument that guarantees such an object or value.