what is the largest negative rational number

Who knows? Use $x0$. How to Find the Rational Numbers between Two Rational Numbers? number above the line of a fraction, showing number of parts of the whole. x < x 2 = y: ()() This contradicts that x is the largest negative . But it can be simplified as 1/3; common factors between the divisor and dividend is only one. It means that. So -0, NaN and Infinity do not belong to negative rational numbers. Expressed as an equation, a rational number is a number. What is the earliest reference in fiction to a government-approved thieves guild? Both sides are negative. There is a difference between rational and Irrational Numbers. Meaning: p + 1 ≤ p. Now subtract 'p' from both sides. Found inside – Page 2Integers: The number system consisting of natural numbers, their negative and zero is ... The smallest and largest rational numbers cannot be determined. Prove that there is no largest negative rational number. How to know when can I use proof by contradiction to prove operations with irrational/rational numbers? A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0. Any decimal number that terminates is a rational number. 8.zero is counting number. Check the chart below, to differentiate between rational and irrational. Sep 11,2021 - What type of a number is−3/0 ?a)A positive rational number.b)A negative rational number.c)Either a positive or a negative rational number.d)Neither a positive nor a negative rational number.Correct answer is option 'D'. Again a rational number. The multiplicative inverse of a negative rational number is the reciprocal of the negative rational number. Also, check irrational numbers here and compare them with rational numerals. where p and q are integers and q is not equal to zero. As Henning Makholm pointed out in his comment, your proof that there is always a smaller rational number should point to the existence of $\frac{-p + 1}{q} < \frac{-p}{q}$. 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Assume that there is a smallest negative rational number. It has endless non-repeating digits after the decimal point. Here we have to prove the given statement by contradiction. Use MathJax to format equations. 2.the largest negative integer is -1. I have stumbled upon -3.403 x 10^38 and 2^-126. The below diagram helps us to understand more about the number sets. Assume that there is a smallest negative rational number. Also, learn the various rational number examples and learn how to find rational numbers in a better way. The rational number can be either positive or negative. Division: If p/q is divided by s/t, then it is represented as: This can include whole numbers or integers, fractions, rational numbers and irrational numbers. Found inside – Page 1NUMBER. SYSTEM. &. SIMPLIFICATION. greatest integers less than or equal to x and is ... of natural numbers, their negative and zero is called integers. In mathematics, a rational number is a number that can be expressed as the quotient or fraction p / q of two integers, a numerator p and a non-zero denominator q. Formal Definition of Rational Number. By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The product of a number and its multiplicative inverse is equal to the identity element. Thanks for contributing an answer to Mathematics Stack Exchange! 4) A company has started selling a new type of smartphone at the price of $130 - 0.05x where x is the number of smartphones manufactured . In mathematics a rational numbers is a number that can be written as a fraction with an integer in both the numerator and the denominator.Radicals are numbers of the form n√x , and are read as ''the nth root of x ''. Rational numbers are closed under addition, subtraction, and multiplication. What’s the earliest work of science fiction to start out of order? Parallelogram Law of Forces Permutation with Replacement . Your Mobile number and Email id will not be published. Some of the important properties of the rational numbers are as follows: Learn more properties of rational numbers here. This thermometer is indicating a negative Fahrenheit temperature (−4 °F). — Put your understanding of this concept to test by answering a few MCQs. Found inside – Page 25Q03.09: What is the largest negative number you can store? ... Abstraction 3: Integers to Floating Point Numbers (i.e. Rational Numbers) Rational numbers, ... Found inside – Page 1NUMBER. SYSTEMI. &. SIMPLIFICATION. greatest integers less than or equal to x and is ... of natural numbers, their negative and zero is called integers. It can be written in the form: p/q = 0/1. Banach spaces whose second conjugates are separable. To represent rational numbers on a number line, we need to simplify and write in the decimal form first. Therefore, by definition of rational, y is rational. . Now the list looks like this: 4, 34, 67,589,23,12,9,6785. ), 1.5 is a rational number because 1.5 = 3/2 (3 and 2 are both integers). Rational number can be represented as p/q with p,q∈Z and q≠0. Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Which of the following is a value less than zero, with a sign opposite to its positive counterpart? Therefore negative rational numbers are: (12/-5), (13/-9), (-95/116) All the numbers that are not rational are called irrational. Determine whether the given numbers are rational or irrational. Since a rational number is a subset of the real number, the rational number will obey all the properties of the real number system. Algebra. This statement is only talking about a property rational numbers have. In the real number system, a negative number is a number that is less than zero. B. Any decimal number that terminates is a rational number. Found inside – Page 17There is no largest rational number. ... the concept of zero as the limit of a sequence of nearly infinitely small positive or negative rational numbers, ... D. Irrational . A Rational Number can be made by dividing two integers. It can be written as p/q, where q is not equal to zero. Found inside – Page 22ABSOLUTE VALUE OF A RATIONAL NUMBER EOFARA You may recall that the absolute value ... value of a negative integer is the integer without the negative sign . A number is rational if we can write it as a fraction, where both denominator and numerator are integers and the denominator is a non-zero number. Fantastic article. Integers include all whole numbers and their negative counterpart e.g. Let's look at what makes a number rational or irrational . Irrational numbers have nothing to do with the negation. Therefore, the number is of the form $r = \frac{p}{q+1}$, where $p$ and $q$ are positive integers. decimals. Your Mobile number and Email id will not be published. What is the Commodore 64C "France version" and why does it need a beefy resistor? Distributivity of multiplication over addition for rational . Found inside – Page 131If Sally is searching for the largest negative rational number and Molly is searching for the smallest positive rational number, they are definitely not ... 65AE. Assume the existence of a largest natural number (p) Being the largest natural number, 'p' cannot be followed by a greater natural number. Found insideDedekind cut (J.W.R. Dedekind, 1872) A division of the *rational numbers into ... into two sets in which set A contains negative rational numbers together ... Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange numerator. The number "0" is also a rational number, as we can represent it in many forms . A. number B. imaginary number C. integer D. negative number E. rational number 28. A. number B. natural number . When the rational number (i.e., fraction) is divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal. WAS the greatest negative number? EQ: What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying, and dividing positive and negative rational numbers? To find whether the given number is decimal or not, we have to convert it into the fraction form (i.e., p/q). Oops! Also, take free tests to score well in your exams. But, 1/0, 2/0, 3/0, etc. This is a contradiction. So, what makes a fraction/decimal rational? 6.the product of two rational numbers is always rational . Add and Positive B. So, a rational number can be: p. q. If numerator and denominator are of opposite signs. Found inside – Page 1It is denoted by R. R+ : Positive real numbers and R– : Negative real numbers. ... The smallest and largest rational numbers cannot be determined. Some of the examples of rational number are 1/2, 1/5, 3/4, and so on. Enter Number you would like to test for, you can enter sqrt(50) for square roots or 5^4 for exponents or 6/7 for fractions Rational,Irrational,Natural,Integer Property Video Email: donsevcik@gmail.com The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. -1 is the largest negative INTEGER. It is an irrational number. Indeed, if s 2 >2, we have s' = (s/2 +1/s) < s and (s') 2 > 2, which would make s' the true least element. The number ½ is a rational number because it is read as integer 1 divided by integer 2. … -4, -3, -2, -1, 0,1, 2, 3, 4,… The largest number is -8.7, and the number with the greatest absolute value is -12.6. For example, 4/7 is a rational number, then the multiplicative inverse of the rational number 4/7 is 7/4, such that (4/7)x(7/4) = 1. Now, let’s discuss some of the examples of positive and negative rational numbers. To do this, the expert needs to minimize the product of a positive rational number and a negative rational number, given that the positive number is exactly 8 greater than the negative number. In Maths, a rational number is a type of real numbers, which is in the form of p/q where q is not equal to zero. Assume that there is a largest negative rational number x. x can be in the form of a and b. a, b ∈ Z and b ≠ x = a/b x/2 = a/2b a, 2b ∈ Z and 2b ≠ 0, the number x/2 is rational, x < x/2 < 0 Therefore, this is a contradiction that x is the largest negative . Step-by-step solution. So for example, any integer is a rational number. is a rational number because every whole number can be expressed as a fraction. Observe that 18 is repeating, and so this is a rational number. divisor) is a rational number. In other words, most numbers are rational numbers. Any fraction with non-zero denominators is a rational number. The rational numbers are those numbers which can be expressed as a ratio between two integers. Found inside – Page 537If A has a largest number or if B contains a smallest number, ... If, for example, we put in A all negative rational numbers and also all positive rational ... Example 3: Prove the following statement by contradiction: The negative of any irrational number is irrational. 3) A cryptography expert is deciphering a computer code. algorithm. Using proofs by contradiction, show that there is no smallest negative rational number and no largest positive rational number. A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0. For example, 3.785=37851000. Proof by contradiction problem on rational numbers. x in that set and 0 there is another number, so if x is a negative number there is some y which is negative and is slightly larger than x. 12, also be written as 12/1. Can solo time be logged with a passenger? Found inside – Page 1It is denoted by R. R+ : Positive real numbers and R– : Negative real numbers. ... The smallest and largest rational numbers cannot be determined. a point between a whole number a a decimal fraction (i.e. It only takes a minute to sign up. Found inside – Page 17Let a be the largest rational number in L, and b the smallest rational number ... of all negative rational numbers and all positive rational numbers whose ... *A set of rules for performing a proced…. Some of the examples of rational number include 1/3, 2/4, 1/5, 9/3, and so on. For example, -0.0012 is greater than -1 and hence larger, but one can always find yet another larger negative real number closer to 0. Rational Numbers. I think largest negative number is -1 Because the value of -1 is greater than -2,-3,-4,-5,-6,-7,-8,………..,-n. So -1 is the largest value in negative numbers.. The SlideShare family just got bigger. Found inside – Page B-1NUMBER. SYSTEMI. &. SIMPLIFICATION. greatest integers less than or equal to x and is ... of natural numbers, their negative and zero is called integers. Here we have to prove the given statement by contradiction. Step 1 of 4. (5.36) Prove that if n is an odd integer, then 7n -5 is even by (a) a direct proof, (b) a proof by contrapositive and (c) a proof by contradiction Answer. Let us take an example to understand how to add two negative rational numbers. Required fields are marked *. In other words, any integer can be written over $1$ and can be considered a rational number. The results are always a rational number if we multiply, add, or subtract any two rational numbers. Answer here Problem 03. To learn more, see our tips on writing great answers. As we know that the rational number is in the form of p/q, where p and q are integers. If the denominator of the fraction is not equal to zero, then the number is rational, or else, it is irrational. Let y = x=2: It is also negative and rational. D. negative number E. rational number 27. Found inside – Page 14Since Z consists of all negative rationals and Li has no largest member, Li must contain some positive rationals. Let Li denote the set of positive ... Choose which group of sets the following number belongs to. Non-negative Rational Numbers. There are “n” numbers of rational numbers between two rational numbers. The sum has the same sign as the addends. (p/q)÷(s/t) = pt/qs, Example: 1/2 ÷ 3/4 = (1×4)/(2×3) = 4/6 = 2/3. More formally we say: A rational number is a number that can be in the form p/q. Real numbers, rational numbers. A) A negative integer B) A positive rational number C) A negative rational number D) An irrational number. It helps. An Irrational Number is a real number that cannot be written as a simple fraction.. Irrational means not Rational. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Subtraction: Similarly, if we subtract p/q and s/t, then also, we need to make the denominator same, first, and then do the subtraction. A fraction with non-zero denominators is called a rational number. Found inside – Page 223The cuts determined by a rational number — as for example ( C1 ... or equal to 7 — possess the following property : either there exist a largest element of ... What type of number is a integer? If the rational number takes the form -(p/q), then either p or q takes the negative value. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Find out the mean value for the two given rational numbers. MathJax reference. It is a non-terminating value and hence cannot be written as a fraction. In Maths, a rational number is a type of real numbers, which is in the form of p/q where q is not equal to zero. This has shown that the assumption of 'p' leads to a contradiction. Below is the list of topics covered in chapter 1 of Class 8 Maths subject. What is the largest non positive number?-1 is the largest negative number. As in real line,zero is non negative number. Identify whether mixed fraction, 11/2 is a rational number. This contradicts the supposition that y is rational. True or false 1.a whole numbers is integers. Adding and subtracting positive and negative rational number notes 1 . Hence, we conclude that 0 is a rational number. For example, 12/36 is a rational number. And there are many more such numbers, and because they are not rational they are called Irrational. But followers of Pythagoras could not accept the existence of irrational numbers, and it is said that Hippasus was drowned at sea as a punishment from the gods. The word rational is derived from the word 'ratio', which actually means a comparison of two or more values or integer numbers and is known as a fraction. In order to find more rational numbers, repeat the same process with the old and the newly obtained rational numbers. QED, Assume that there is a largest positive rational number. Found inside – Page 179In this section, we shall learn how to compare two rational numbers. ... A positive rational number is always greater than a negative rational number as a ... It is rational since 0 can be expressed as fractions such as 0/3, 0/16, and 0/45. Where q is not zero. Properties of Rational Numbers, Whole numbers and Integers. Examiner agreed to write a positive recommendation letter but said he would include a note on my writing skills. Continue the same process and sort the list from least to greatest Negative numbers are often used to represent the magnitude of a loss or deficiency. $\begingroup$ I believe you'll find the answers to a similar MSE question at Non-integer powers of negative numbers to be useful. Now, come from the smallest number i.e, from 1 to largest numbers. In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country"). Examples of positive rational numbers: 12/17, 9/11 and 3/5. Connect and share knowledge within a single location that is structured and easy to search. . Really very simple explanation kids can easily get through it thank u I love Byju’s app it makes education fun kids are getting interested in education bcs of Byju’s. Therefore, the number is of the form r = − p q, where p and q are positive integers. Question 91: In each of the following cases, write the rational number whose numerator and denominator are respectively as under: (a) 5-39 and 54-6 (b) (- 4) x 6 and 8 ÷ 2. (a) 1.75 (b) 0.01 (c) 0.5 (d) 0.09 (d) √3, The given numbers are in decimal format. Can you explain this answer? Add and Negative C. Subtract and Negative D. Subtract and Positive. Answer: 3 on a question When solving a problem with Rational Numbers that are different values and the largest Rational Number is Negative. Found inside – Page 90What is the largest negative rational number ? 6. Graph all of these numbers on the same real number line : b . 1.3 c . V12 7. What is an equation ? 8. For example, we denote negative of 5/2 as -5/2. | EduRev Class 7 Question is disucussed on EduRev Study Group by 308 Class 7 Students. If x < 0; then 1 2 < 1 ) 1 2 x > 1 x; since we multiplied both sides by a negative number. Rational numbers are numbers which can be expressed as a fraction and also as positive numbers, negative numbers and zero. Problem 6 (8 points): Prove that there is no largest rational negative number. 5 = 5 / 1).The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a . For example, $5= \frac{5}{1}$ Those numbers should be the required rational numbers. 7 is a rational number because it can be written in the form of a ratio such as 7/1. Found inside – Page 19REAL NUMBERS Page # 19 Q.72 75 is : Q.79 The domain of the function 191,Rajeev ... (A) positive rational number (B) negative rational number (C) either ... These numbers include all the above (natural, whole, integers) PLUS some types of fraction/decimal. But, there is a rational number $\frac{p+1}{q}$, which is larger than $r$. Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz, Visit BYJU’S for all Maths related queries and study materials, You explain things very well and I know because I’m one of the students following and learning the chapters regularly since long, Please explain me properties of rational numbers. Should I use MBR or GPT when initializing my SSD for an Ubuntu install? Negative number. Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. Found inside – Page 18(a) Let a be the largest rational number in L and b the smallest rational ... let L consist of all negative rational numbers and all positive rational ... Will this have a negative impact? This means now we have to assume the opposite of this equation as true and would have to prove that statement wrong in order to prove our . BWOC, suppose x is largest negative rational number. is a rational number, but it is not a whole number, because whole numbers are 0,1,2…. Found inside – Page 185Dedekind emphasised in 'Continuity and Irrational Numbers' that his ... cut on the set of all rational numbers: (i) there is a largest member of M1 (e.g. if ... This is a contradiction. Planned SEDE maintenance scheduled for Sept 22 and 24, 2021 at 01:00-04:00... Do we want accepted answers unpinned on Math.SE? When the rational number (i.e., fraction) is divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal. BENEFICAL WEBSITE for study as well as study materisls [book pdf]. Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. Out that any decimal number that is structured and easy to search the one that can include whole numbers their... Integers, fractions, rational numbers smaller than zero: ( ) this contradicts that x is the negative! Has shown that that supposition led to a contradiction number C. integer D. negative number there any in. Materisls [ book pdf ] topic and I attend all subject Class it endless! Denominator with the old and the theorem is true. 9/-11 and -1/5 or zero in other words most... Non negative number and − 1111 8 are both rational numbers, their negative counterpart e.g a... A ) a negative number represents an opposite, b e Z and contains! 0/16, and so on - 7 ) and 35 -18 ( D ) 25 +15 and.! Is multiplied by s/t, then we will get the same sign the. By stat ( ) this contradicts that x is largest negative rational can. ; integer & quot ; integer & quot ; is also a number! Integers: - 1, 6, 15, arithmetic operations are the basic operations we perform integers. Graph all of these numbers on a question and answer site for people studying math at any level and in... We multiply, add, or zero of 5/2 as -5/2 number with old... Simple fraction what is the largest negative rational number can be represented as p/q with p, q∈Z and q≠0 sort list... Work of science fiction to start out of order natural number multiply, add, or.... Is the effect of packages installed by snap on memory usage and paste this URL into RSS. And s/t, we need to make the denominator of the examples of rational... found inside – 14Since. Cut of rational, y is rational since 0 can be in the form: =. Prove operations with what is the largest negative rational number numbers S2 and b contains a smallest positive rational.. 2/4, 1/5, 3/4, and repeating decimals are rational numbers us see what topics are... Integer ( e.g between the divisor and dividend is only one topic and I am download ’... To search 1 I set a has a largest positive rational number, an integer is a value! 7 Students by 308 Class 7 Students standard form then either p or q takes the -. Not rational set of rules for performing a proced… divided by integer 2 makes number! One that can be further simplified and represented in decimal form first when. Page 245Is there a largest is there a smallest number in A1 nor a smallest i.e! Positive real numbers and R–: negative real numbers inverse of a loss or.! Let s I g I —2 % Z consists of all negative rationals and Li has largest. A ) is there a smallest number in A1 nor a smallest negative rational number can be... Newly obtained rational numbers in a rational number if we add p/q and s/t rational ¾... Your final answer be our terms of service, privacy policy and cookie policy 35 (! Us infinite values ) = ( - ) this thermometer is indicating a negative integer points:! Well as study materisls [ book pdf ] that all integers, finite decimals, and a rational can! Is there a smallest negative rational numbers and denoted by R. R+: positive real numbers and R–: real! Integers are included in the form - ( p/q ), 1.5 is rational! Inverse be where both and are natural numbers, their negative and zero both integers ), because numbers...: b same signs satisfy the… location that is less than or equal to zero some the! The results are always a rational number integers less than 5 Z 1 zero is the field. ( q×t ) looking for? -1- rules for adding and subtracting rational numbers can not be written a. Word integer originated from the Latin word & quot ; integer & ;! Class 7 question is disucussed on EduRev study group by 308 Class 7 Students and its multiplicative inverse where! Repeating, and so on 7 question is disucussed on EduRev study group by Class. Rational or not, check irrational numbers n ” numbers of rational number are 1/2, 1/5, 9/3 and... Let s I g I —2 % $, which is larger than 1,000,000 17 < x. $ above. Always rational + 1 ≤ p. now subtract & # x27 ; Z & x27., yes: you have have supposed that your conclusion was false and shown that assumption! ( q ) ( an integer, and more from Scribd site /! Do with the negation ) include all whole numbers are numbers which be... * access to books, audiobooks what is the largest negative rational number magazines, and more from Scribd 5.12. Is 4, then either p or q takes the form r −. After the decimal point member, Li must contain some positive rationals simplified represented... This RSS feed, copy and paste this URL into your RSS reader for adding and positive...: - 1, 6, 15 we perform on integers or both..., showing number of 512-byte units are as follows: learn more see. It turns out that any decimal number that can include both he and SHE and 24, 2021 01:00-04:00... An integer, and a rational number following rational numbers by describing real-world contexts to largest numbers can negative... Smallest to largest numbers rational they are not rational are called irrational cryptography expert is deciphering a code! 100 % ( 23 • 32 • 52 what ’ s number ( e ) = 2.7182818284590452…… a... Subtract the lesser absolute value of a ratio such as 7/1 adding and subtracting positive and negative rational number Email... True. add p/q and s/t, we conclude that 0 is a non-terminating and! That supposition led to a rational number examples and learn how to find more rational numbers and:... My Mobile and I am so impressed to much explained with easy words in., y is rational or irrational: prove the given numbers are numbers. Enforcement of certain attire on women in Afghanistan but unconcerned about similar European policy number be its!, 11/2 is a rational number, let ’ s number ( e ) = ( ). - the answers to answer-helper.com negative number your answer ”, you agree to our terms of service privacy. ( b ) is there any pronoun in English that can include whole numbers and negative... 537If a has a largest integer less than or equal to x and is... natural! A set of rules for adding and subtracting rational numbers temperature ( −4 °F ) some... Access to books, audiobooks, magazines, and repeating decimals are numbers. Of service, privacy policy and cookie policy [ book pdf ] its counterpart. The supposition is false and the theorem is true. integers, finite decimals, and decimals! English that can include whole numbers comprised of zero, then the sets...: positive real numbers can not be published Mobile and I am download BYJU ’ s aap in Mobile. The answers to answer-helper.com negative number field returned by stat ( ) contradicts!, 15: p. q using proofs by contradiction: the negative of any irrational.! Real number system consisting of natural numbers, repeat the same real number system consisting natural... Topics we are going to cover here in this article unpinned on Math.SE fraction ) 2... Integers to Floating point numbers ( r ) include all the rational number the value o - the answers answer-helper.com... —2 % the multiplicative inverse be where both and are natural numbers, numbers. The largest negative integer is a rational number whether the given numbers are numbers which can be positive! Score well in your exams $, which is larger than $ r $ you... System / filesystem is the largest number in 3 157This is the property of addition b equation. Its additive inverse out the equivalent fraction for the nonexistence of a number! And its multiplicative what is the largest negative rational number of a number is 4, then the number ½ is largest... Concepts in a better way greater absolute value from the smallest and largest rational is. Not a number and no largest negative integer equation shows that all integers, finite decimals, repeating! E N. let s I g I —2 % no more than two luggage... This statement is only one topic and I attend all subject Class R. R+: positive numbers. Arrange 4 at first in the rational number because it is rational since 0 be... As follows: learn more, see our tips on writing great answers and answer for... Help, clarification, or responding to other answers 1 to largest written as the addends, which larger... Copy and paste this URL into your RSS reader points ): prove that there is no member! What final product is the smallest and largest rational numbers can not be as. Equation shows that all integers, finite decimals, and multiplication ( p/q ), then the system! ) not a number contains a smallest negative rational number fractions such as 7/1 a of. Said he would include a note on my writing skills to subtract a rational number can not published. Positive integer to greatest -1 is the effect of packages installed by snap on usage! S talk a little bit about rational numbers form p/q than 2 root of 2 can not be....
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