If I understand the question correctly then a is a proper subset of u.
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Some decimals are. Counting numbers are a proper subset of decimals.
Counting numbers are a proper subset of whole numbers which are the same as integers which are a proper subset of rational numbers.
All counting numbers ARE (not is!) a proper subset of the set of whole numbers.
The set of counting numbers is a proper subset of the whole number. The latter includes negative counting numbers. Also, there is no consensus as to whether 0 belongs to counting numbers or whole numbers.
The set of counting numbers is the positive integers. The set of whole numbers is the positive integers plus zero. The term "natural numbers" has been used interchangeably with both of those sets.