Line 10: Line 10:
 
'''·''' Suppose x ∈ A
 
'''·''' Suppose x ∈ A
  
1. Say what it means for x to be in A;
+
|1. Say what it means for x to be in A
2. Mathematical details;
+
|2. Mathematical details
3. Conclude that x satisfies what it means to be in B;
+
|3. Conclude that x satisfies what it means to be in B
 +
 
  
 
'''·''' Conclude x∈B
 
'''·''' Conclude x∈B

Revision as of 07:48, 25 November 2012

Proving one set is a subset of another set

Given sets A and B we say that is is a subset of B if every element of A is also an element of B, that is,

x∈A implies x∈B


Basic Outline of the Proof that A is a subset of B:

· Suppose x ∈ A

|1. Say what it means for x to be in A |2. Mathematical details |3. Conclude that x satisfies what it means to be in B


· Conclude x∈B

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

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