A set with members allowed to appear more than once I'm looking for a definition for a set which its members could be appeared more than once!
for example: $$D=\{1,1,2,4,6,6\}$$
Could we call this a set?

It looks like the "word" you're looking for is "Multiset":
From Wikipedia (entry linked):

In mathematics, the notion of multiset (or "bag") is a generalization of the notion of set in which members are allowed to appear more than once. For example, there is a unique set that contains the elements a and b and no others, but there are many multisets with this property, such as the multiset that contains two copies of a and one of b or the multiset that contains three copies of both a and b. The term "multiset" was coined by Nicolaas Govert de Bruijn in the 1970s. [Boldface mine.]

Historically:

The use of multisets in mathematics and beyond predates the name "multiset" by many centuries: Knuth (1998) attributes the first study of multisets to the Indian mathematician Bhascara Acharya (circa 1150), who described permutations of multisets.

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*Knuth, Donald E. (1998). The Art of Computer Programming – Vol. 2: Seminumerical Algorithms (3rd edition ed.). Addison Wesley. p. 694. Knuth also lists other names that were proposed for multisets, such as list, bunch, bag, heap, sample, weighted set, collection, and suite.


