Q16 of 18 Page 88

Explain when a system of axioms is called consistent?

The Euclid’s axioms are as follows:

• First Axiom: Things which are equal to the same thing are also equal to one another.


• Second Axiom: If equals are added to equals, the whole is equal.


• Third Axiom: If equals are subtracted from equals, the remainders are equal.


• Fourth Axiom: Things which coincide with one another are equal to one another.


• Fifth Axiom: The whole is greater than the part.


These system of axioms are consistent as they all hold true and do not contradict each other. If these any of these axioms contradict any other, they would become inconsistent.


Consistent means done in the same way over time, as to be fair or accurate.


And Euclid’s axioms have held true over time.


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