Prove that if x is a real number then [2x] = [x] + [x + ½ ], Mathematics

Prove that if x is a real number then

[2x] = [x] + [x + ½ ]

Ans: Let us consider x be any real number. It comprises two parts: integer and fraction. With no loss of any type of generality, fraction part can all time be made +ve. For instance, -1.3 can be written as -2 + 0.7.

Here now write x = a + b, and [x] = a (integer part only of the real x). The fraction part b requires to considered in two cases: 

0 < b < 0.5 and 0.5 ≤ b < 1.

Case 1: 0 < b < 0.5; In this case [2x] = 2a, and [x] +[x + .5] = a + a = 2a

Case 2: 0.5 ≤ b < 1; In this case [2x] = 2a + 1, and [x] +[x + .5] = a + (a + 1) = 2a +1

Hence [2x] = [x] + [x + .5]

Posted Date: 5/3/2013 4:00:00 AM | Location : United States







Related Discussions:- Prove that if x is a real number then [2x] = [x] + [x + ½ ], Assignment Help, Ask Question on Prove that if x is a real number then [2x] = [x] + [x + ½ ], Get Answer, Expert's Help, Prove that if x is a real number then [2x] = [x] + [x + ½ ] Discussions

Write discussion on Prove that if x is a real number then [2x] = [x] + [x + ½ ]
Your posts are moderated
Related Questions
draw a line OX=10CM and construct an angle xoy = 60. (b)bisect the angle xoy and mark a point A on the bisector so that OA = 7cm



Comparison - the difference between two groups or numbers, namely, how much one is greater than the other, how much more is in one group than in the other. (e.g., if Munna has

A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.

The calculation of two complementary angles are in the ratio of 7:8. Determine the measure of the smallest angle. a. 84° b. 42° c. 48° d. 96° b. Two angles are compl

Multistage sampling Multistage sampling is similar to stratified sampling except division is done on geographical/location basis, for illustration a country can be divided into


Example  Reduce 24/36 to its lowest terms. 24/36=12/18=6/9=2/3. In the first step we divide the numerator and the denominator by 2. The fraction gets reduced

This topic is specified its own section for a couple of purposes. Firstly, understanding direction fields and what they tell us regarding a differential equation as well as its sol