# Symbol for the number of elements in a set

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

• $\#\{x \in TP : x > threshold\}$ or $|\{x \in TP : x > threshold\}|$ May 22, 2019 at 21:57

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.
• $$|C|$$ (using absolute value signs)
• $$\#C$$ (using a number sign)
• $$\text{card}(C)$$ (as a function itself, effectively)
With $$C$$ defined as above, $$|C|$$, the cardinality of $$C$$, would represent the number of elements $$x$$ in $$TP$$ such that $$x>\text{threshold}$$. Written out fully: $$|C|=|\{x\in TP\mid x>\text{threshold}\}|$$