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"Definition and Proposition" Proof PPT Courseware 3
(1) Definition:
Generally, a sentence that can clearly define the meaning of a name or term is called the definition of the name or term.
(2) Can you give the definition of the following names?
Irrational numbers: Infinite non-repeating decimals are called irrational numbers.
Pressure: The pressure per unit area is called pressure.
Define "proposition"
Compare the expression forms of the following sentences. Which one makes a judgment about the matter? Which ones don’t make judgments about things?
(1) Birds are animals.
(2) If a2=b2, then a=b.
(3) 0.33 is an irrational number.
(4) The two straight lines are parallel and have equal angles.
Statement:
Generally speaking, a sentence that makes a correct or incorrect judgment about a certain thing is called a proposition.
The current proposition can be seen as consisting of two parts: the proposition (condition) and the conclusion (conclusion). The proposition is the known matter, and the conclusion is the matter deduced from the known matter.
Example: Find the conditions and conclusions of the proposition:
Two triangles with three corresponding equal sides are congruent.
Condition: The three sides of the two triangles are equal,
Conclusion: These two triangles are congruent.
In the same triangle, equal sides correspond to equal angles.
Condition: Two sides of the same triangle are equal,
Conclusion: The angles they subtend are also equal.
If two sides of the same triangle are equal, then the angles they subtend are also equal.
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