Irrational + 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. All we have to do now is prove the assumption, which I think is easier. edit: I just saw tongos' proposition, which I think is better than mine.
Square Root of an Irrational Number is Irrational - Physics Forums
2012年2月23日 · The square root of an irrational number is irrational because it cannot be expressed as a fraction of two integers. This is because irrational numbers have decimal representations that never end and never repeat in a pattern, making it impossible to write them as a ratio of two integers.
Showing that tan(1) is irrational - Physics Forums
2019年2月11日 · An irrational number is a real number that cannot be expressed as a ratio of two integers. In other words, it cannot be written in the form a/b where a and b are integers. How do you prove that a number is irrational? To prove that a number is irrational, you must show that it cannot be written as a ratio of two integers.
Prove the Irrationality of the Golden Ratio & Phi - Physics Forums
2007年10月4日 · Why is the Golden Ratio considered irrational? The Golden Ratio is considered irrational because it cannot be expressed as a fraction of two integers. It is a non-repeating, non-terminating decimal and its digits go on infinitely without forming a pattern. What is the proof of the irrationality of the Golden Ratio?
Natural constants: are they irrational numbers? - Physics Forums
2010年12月12日 · A natural constant is considered irrational if it cannot be expressed as a ratio of two integers. This means that the decimal representation of the constant is non-terminating and non-repeating. For example, the value of pi (π) is an irrational number because it cannot be expressed as a fraction. Why are some natural constants irrational?
Proving Irrationals Are Dense in the Reals - Physics Forums
2010年7月29日 · Some previous results that I'm using is that a rational plus an irrational is irrational, and that a rational multiplied by an irrational is also irrational. So since I knew that for any r that is an element of Q, and x, y that are elements of R, then x < r < y. Or that the rational numbers are dense in R. So consider an irrational number v ...
*Proof* Sum of Rational and Irrational Numbers - Physics Forums
2009年1月27日 · Homework Statement Prove by contradiction: If a and b are rational numbers and b != 0, and r is an irrational number, then a+br is irrational. In addition, I am to use only properties of integers, the definitions of rational and irrational numbers, and algebra. You guys should also know that...
Prove square root of 3 is irrational - Physics Forums
2010年3月23日 · A number is considered irrational if it cannot be expressed as a fraction of two integers, meaning it has an infinite number of non-repeating digits after the decimal point. Why is it important to prove that the square root of 3 is irrational?
Discrete Math irrational and rational numbers proof - Physics …
2011年9月18日 · Prove by contradiction. Your proof should be based only on properties of the integers, simple algebra, and the definition of rational and irrational. If a and b are rational numbers, b does not equal 0, and r is an irrational number, then a+br is irrational. Homework Equations rational numbers are equal to the ratio of two other numbers
Irrational numbers aren't infinite. are they? - Physics Forums
2016年12月28日 · No, irrational numbers are not limited in quantity. While they cannot be expressed as a simple fraction, they can still be infinite in quantity. Why are irrational numbers considered to be non-infinite? Irrational numbers are considered non-infinite because they do not follow a repeating pattern and cannot be expressed as a finite or infinite ...