what are the 6 fields axioms of real number? what arethe 3 equality axioms of real numbers? and what are the 5 axioms of order? pls...help me with my homeworks

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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1) The reflexive axiom of equality:

x = x, for ay real number "x"

Example 100 = 100

2) The symmetric axiome of equality:

If x = y, then y = x

Example: If 1 + 4 = 5, then 5 = 1 + 4

3) The transitive axiom of equality:

If x = y and y = z, then x = z

The axioms of order:

1) Translation invariance of order: x < y => x + z < y + z, for any x and y real numbers

Example: 2 < 3 => 2 + 4 < 3 + 4 <=> 6 < 7

2) The transitivity axiome of order: x < y and y < z => x < z

3) The trichotomy axiome of order: x < y and y < x  => x = y

4) The scaling axiome of order:

If x < y and z> 0 => x*z < y*z

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