[Math] Symbol for the number of elements in a set

notation

I would like to express below concisely and mathmatically

  1. TP is a set of real numbers

  2. $$C = \{ x \in TP : x > threshold \}$$

  3. c_count = len(C)

Basically, in English, I want to count the number of numbers in TP is greater than threshold

Best Answer

Since $C$ is defined as a subset of $TP$ based on the premise of being greater than some threshold, then, if $C$ is finite, you can refer to "cardinality" - it is a measure of how many elements are in a set. It gets murkier for infinite sets, but for finite sets, the cardinality of a set is just the number of elements in the set.

How would one denote cardinality? There are several conventions I've seen:

  • $|C|$ (using absolute value signs)
  • $\#C$ (using a number sign)
  • $\text{card}(C)$ (as a function itself, effectively)
Related Question