LEARN · EXPLAIN · REVISE

How many elements are in this real solution 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=\{x\in\mathbb R:x^2+1=0\}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Check whether any real value can satisfy the condition.

Hint 2

A real square cannot be negative.

Worked solution

The requested value is 0.

Checks and common pitfalls: The empty set is different from the singleton containing zero.

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.