Mathematical expression of the number of names fulfilling the condition

Question

I have an example where a total of 2200 names are entered.

1. Each name has an assigned percentage value from 0% to 100%.
2. The total number of names with a value above 88% is 459.

I need to formulate this in a mathematical way in a formula that will point out that it is precisely the 459 names which are those we look for.

Thank you for any help.

Answer 1

You can use the following expressions: $$A=\{(x_i,y_i),i=\overline{1,2200},0\le y\le100\}\\|A|=2200\\B=\{(x_i,y_i)\in A,y_i\gt88\}\\B\subset A\\|B|=459$$ You might be able to skip some of the lines. An alternative notation for cardinality is "$\#$".