Is it true that for any sequence of irrational numbers <mo fence="false" stretchy="false">{

vasorasy8 2022-07-09 Answered
Is it true that for any sequence of irrational numbers { h n } converges to zero in [ h , h ] both α + h n and α h n and α + h n and α h n are always irrationals ?
You can still ask an expert for help

Want to know more about Irrational numbers?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

SweallySnicles3
Answered 2022-07-10 Author has 21 answers
Most certainly not.
In fact, take any sequence q n of rational numbers in [ α h , α + h ] that converges to α [ 1 ]. Now, define h n = q n α. Then,
h n is in [ h , h ].
h n converges to 0.
for all n N , hn is irrational
However, α + h n = q n , which means that α + h n is always rational.

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions