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Is there a smallest positive rational number?
1/infinity? * * * * * Nice idea but unfortunately that is not a rational number, which is defined as the ration of two integers, x/y where y > 0. Since infinity is not an integer, the suggested ratio is not a rational number. The correct answer is that there is no such number. If any number laid claim to being the smallest positive rational, then half of that number would have a better claim. And then a half of THAT number would be a positive rational that was smaller still. And so on.
Is 0.678667866678 rational or irrational number?
As written, it is a terminating decimal, which can be converted to a quotient(fraction) . Hence it is rational. However, if 0.678667866678.... then it is recurring to infinity . , Since it will not convert to a quotient/fraction , then it is irrational.
Is the set of all rational numbers continuous?
Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.
Is 1.234 is a not rational number?
First of all , do not use the phrase ' not rational' . The word in the English language, and mathematics is 'IRRATIONAL'. Net 1.234 is rational; it can be converted to a ratio(fraction). For irrational numbers the decimals go to inifinity and there is no regular order in the decimal digits. 'pi' is probably the most well known irrational numbers at pi = 3.141592654... The three terminl dots/stops indicate to mathemticians, that the number goes to infinity. Notice also, there is no regular order of digits in the decimal moiety. Since the number given ends at '4' , then it does not go to infinity, hernce it is rational . To convert to a ratio (fraction) 1.234 = 1 234/1000 Cancel down by '2' 1 117/500 (THis is the fraction in its lowest terms).
Is the product of a rational number and a rational number a rational number?
yes
Which is the biggest rational number?
Infinity
Is a real number sometimes a rational number?
Infinitely rarely, a real number is also a rational number. (There are an infinite number of rational numbers, but there are a "much bigger infinity" of real numbers.)
Is there a smallest positive rational number?
1/infinity? * * * * * Nice idea but unfortunately that is not a rational number, which is defined as the ration of two integers, x/y where y > 0. Since infinity is not an integer, the suggested ratio is not a rational number. The correct answer is that there is no such number. If any number laid claim to being the smallest positive rational, then half of that number would have a better claim. And then a half of THAT number would be a positive rational that was smaller still. And so on.
What is the Next to rational and irrational number?
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
What is the thinking about The density of numbers on the number line of rational and irrational number?
There are countably infinite rational numbers. That is, it is possible to map each rational number to an integer so that the set has the same number of elements as all integers. This is the lowest order or infinity, Aleph-null. The number of irrationals is a higher order of infinity: 2^(Aleph-null). This is denoted by C, for continuum. There are no orders of infinity between Aleph-null and C.
Is the number 3 rational irrational both rational and irrational or neither rational?
'3' is RATIONAL. All numbers are RATIONAL except those were the decimal goes to infinity AND the decimal digits are NOT in any regular order. pi = 3.1419592.... is probably the most well known IRRATIONAL number. Also the Square Roots of Prime numbers. NB 3.333.... recurring to infinity is RATIONAL, because it can be converted to a RATIO/Fraction.
Is every real number either a rational number or a irrational number?
Yes. A real number is any comprehendable number, from negative infinity to positive infinity. A rational number is any number that can be the answer to a division equation; an integer, fraction, or a decimal. An irrational number is any number that cannot be expressed as a fraction; such as exponents.
Are there more rational numbers or irrational Numbers?
No. The number of irrationals is an order of infinity greater.
Is there more rational numbers then irrational?
No. There are infinitely many of both but the number of irrational numbers is an order of infinity greater than that for rational numbers.
Is There fewer rational numbers than irrational numbers.?
Yes. The infinity of rational numbers has the same size as the natural numbers, said to be "countable". The infinity of real numbers (and therefore, also of irrational numbers) is a larger infinity, said to be "uncountable".
Why the denominator of rational number should not be equal to zero?
To divide any number by zero will give infinity and therefore an error.
Is 100000000000.2 a rational number?
Yes, any number whose decimal terminates or has repeating decimals to infinity is a rational number. More precisely, any number that can be expressed as a fraction between two integers is a rational number. In this case 100000000000.2 = 1000000000002/10, or 500000000001/5.
