How Do We Know If Irrational or Transcendental Numbers Repeat?
2014年3月25日 · The discussion centers on the nature of irrational and transcendental numbers, specifically whether they can have repeating decimal expansions. It is established that …
irrational = rational - Physics Forums
2005年3月13日 · Assume that the difference between a rational number and an irrational number is an irrational number. The sum of any such two irrational numbers would be a rational number.
Square Root of an Irrational Number is Irrational - Physics Forums
2012年2月23日 · So, an irrational number is one in which m=q/p does not exist. I understand that part, but then trying to show that the square root of an irrational number is irrational is giving …
Is Pi a rational number in any other base besides base Pi?
2013年7月24日 · Pi is irrational in any base, as its property of being rational is independent of the base used for representation. While it can be expressed differently in various bases, such as …
Is i Rational or Irrational? Decoding the Nature of Imaginary …
2008年7月4日 · The discussion centers on whether the imaginary unit "i" is rational or irrational. It is established that "i" cannot be expressed as a ratio of two integers, leading to the conclusion …
Proving Irrationals Are Dense in the Reals • Physics Forums
2010年7月29日 · Homework Statement Show that the irrational numbers are dense in R. [Hint: Use the fact that sqrt(2) is irrational.]Homework Equations Book already proved that the …
Is there always at least one irrational number between any two …
2008年6月26日 · But again, an irrational number plus a rational number is also irrational. Therefore, there is always at least one rational number between any two rational numbers. …
If a, b are irrational, then is ##a^b## irrational? - Physics Forums
2017年1月13日 · Homework Statement True or false and why: If a and b are irrational, then a b is irrational. Homework Equations None, but the relevant example provided in the text is the …
Irrational Number Raised To Irrational Number - Physics Forums
2021年6月17日 · An irrational number raised to an irrational power can indeed yield a rational result, as demonstrated by the example A = (sqrt {2})^ (sqrt {2}). If A is rational, the problem is …
Constructing Lengths with Irrational Numbers - Physics Forums
2004年12月6日 · The discussion centers on the nature of irrational numbers and their existence in the physical world, questioning how lengths like the hypotenuse of a right triangle can be …