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Default What is the math behind array function

Hello everybody
How an array function calculates? for ex
{sum(1/(countif(range, criteria)} returns the number of non-repeats
I tried to analyse it in the following way, but of no use
CIF ARRY-CIF 1/CIF ARRAY-1/CIF SUM-CIF ARAY-SUMCIF SUM-1/CIF ARAY-1/SUMCIF
Cow 2 2.00 0.50 0.50 2.00 17.00 0.50 3.00
cat 2 2.00 0.50 0.50 2.00 17.00 0.50 3.00
mat 3 2.00 0.33 0.50 3.00 17.00 0.33 3.00
cow 2 2.00 0.50 0.50 2.00 17.00 0.50 3.00
cat 2 2.00 0.50 0.50 2.00 17.00 0.50 3.00
mat 3 2.00 0.33 0.50 3.00 17.00 0.33 3.00
mat 3 2.00 0.33 0.50 3.00 17.00 0.33 3.00

CIF COUNTIF($A$2:$A$8,$A$2:$A$8)
SUM-CIF SUM(COUNTIF($A$2:$A$8,$A$2:$A$8))
Thanks to all
regards
Sridhar
 
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