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- The statement might be viewed as obvious. One example of such an axiom is the Principle of contradiction, which says that a statement and its opposite cannot both be true at the same time in the same place.
- The statement is based on physical laws and can easily be observed. An example for this are Newton's laws of motion
- A logical proposition, given at the start of an argument. This is the modern definition of axiom
Logic can be used to deduce other theorems from the axioms.
Euclid's axioms[change | edit source]
Euclid of Alexandria was a Greek mathematician. Around the year 300BC, he made a list of axioms:
- Two numbers that are both the same as a third number are the same number.
- If A and B are two numbers that are the same, and C and D are also the same, A+C is the same as B+D.
- If A and B are two numbers that are the same, and C and D are also the same, A-C is the same as B-D.
- Two shapes that fill exactly the same space are the same shape.
- If you divide a number by anything more than 1, the quotient (result) will be less than the original number.