LEARN · EXPLAIN · REVISE

How many elements are in this set?

Read the idea, work independently, then explain what changed.

高一必修第一册(A版).pdf · 1.1 · PDF 9 / printed page 2

TOPIC 01

Concept of a set

Build understanding of concept of a set through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

A=\{\varnothing,\{0\}\}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Check the membership rule and count distinct objects.

Hint 2

The two objects inside the outer braces differ.

Worked solution

Check the membership rule and count distinct objects.
Calculate or simplify this relation.
$|\varnothing|=0,\quad |\{0\}|=1,\quad |A|=2$
An empty set can be an element of a different set.

The requested value is 2.

Checks and common pitfalls: An empty set can be an element of a different set.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Apply concept of a set with explicit conditions.
Membership: A set has definite membership and distinct elements.
$x\in A$
Representations: A roster lists members; set-builder notation specifies their domain and condition.
Close with: conditions → representation → reasoning → check.

Expected reasoning: A set has definite membership and distinct elements.
Expected reasoning: A roster lists members; set-builder notation specifies their domain and condition.
Expected correction: Repeated entries do not add elements.