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Elements Of Modern Algebra
- Prove that if is a nonzero rational number and is irrational, then is irrational.arrow_forwardProve that if is a nonzero rational number and is irrational, then is irrational.arrow_forward13. Prove that if and are rational numbers such that then there exists a rational number such that . (This means that between any two distinct rational numbers there is another rational number.)arrow_forward
- Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that a2=3b2. Explain how this proves that 3 is not a rational number.arrow_forwardProve that if a is rational and b is irrational, then a+b is irrational.arrow_forwardProve by induction that if r is a real number where r1, then 1+r+r2++rn=1-rn+11-rarrow_forward
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