Fill in the blanks with correct terms.

A _______ is a collection of things. The things are called ___________of the set.

Question

Fill in the blanks with correct terms.

A _______ is a collection of things. The things are called ___________of the set.

BlackTom AI · Accepted Answer

A set is a collection of distinct objects, so the first blank is "set" and the second blank is "elements."

1. Relevant knowledge points and concepts
- Definition: A set is a well-defined collection of distinct objects considered as an entity.  
- Elements (also called members): The individual objects contained in a set.  
- Notation: If a is an element of set A we write a ∈ A; if not, a ∉ A. Example: For A = {1, 2, 3}, the elements (members) are 1, 2, and 3.

2. Step-by-step reasoning process
- Read the sentence: "A _______ is a collection of things." The standard mathematical term for "a collection of things" is "set." So blank 1 = set.
- Next sentence: "The things are called ___________ of the set." The objects that belong to a set are called its "elements" (or "members"). So blank 2 = elements.

3. Intermediate steps shown explicitly
- Replace blank 1: A set is a collection of things.
- Replace blank 2: The things are called elements of the set.
- Combined filled sentence: "A set is a collection of things. The things are called elements of the set."

4. Why the correct answer is correct
- "Set" is the conventional term in mathematics for a collection.  
- "Elements" precisely names the items inside a set; it is the standard terminology used in definitions, notation, and formal statements.

5. Why other possible words would be incorrect or less precise
- Words like "group" have specific algebraic meanings and are not synonyms for a general collection.  
- "Collection" in the second blank would be circular and unclear.  
- "Members" is an acceptable synonym for "elements," but the given correct answers list "elements," so that form is preferred.

6. Conclusion
- The filled sentence is: "A set is a collection of things. The things are called elements of the set." This matches the provided correct answer ("set and elements" / "set, elements").

Fill in the blanks with correct terms. A _ is a collection of things. The things are called _____of the set.简答题

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Fill in the blanks with correct terms. A _______ is a collection of things. The things are called ___________of the set.简答题