# What is INF in Isabelle

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I found this definition in Isabelle

``````definition (in topological_space) nhds :: "'a ⇒ 'a filter"
where "nhds a = (INF S∈{S. open S ∧ a ∈ S}. principal S)"
``````

What is INF? I can’t find anything in query tab nor can I jump to definition with Ctrl+Click.

### >Solution :

In Isabelle, INF is a constant symbol that represents the positive infinity value. It is typically used in mathematical proofs and reasoning about real numbers. Isabelle has built-in support for reasoning about the real numbers and includes a number of theorems and lemmas about the properties of infinity.

For example, it can be used to express that a certain value is greater than all natural numbers, or that the limit of a certain function approaches infinity.

In Isabelle/HOL, infinity is defined as a type and the notation infinity::’a::linorder_top can be used to represent it.

Additionally, Isabelle also provides the Infinity class, which is a type class for types that have an infinity element.

It’s important to note that Isabelle is a formal verification system and the meaning of infinity is defined in the context of the logic and the proof system being used.