![]() ![]() That are not integers? For example, let us imagine. So negative 7 is definitelyĪ rational number. Represented as negative 7/1, or 7 over negative 1, or Have an infinite number of representations In all of these cases, these areĪll different representations of the number 1, 1 can be represented as 1/1 orĪs negative 2 over negative 2 or as 10,000/10,000. The ratio of two integers is a rational number. And the simple way to thinkĪbout it is any number that can be represented as The concept of infinity is very hard to grasp.Ībout rational numbers. That is not to say the the infinity of irrational numbers is larger than the infinity of rational numbers. The infinity of irrational numbers is more than the infinity of positive integers. See the Peter Collingridge comment below. There are some math concepts that do compare infinities. One infinite is not greater than, less than, or even equal to, another infinite. It is also not correct to say that the numbers between 0 and 1 and the numbers between 0 and 2 are the same. And you can't say that one infinite is more than another infinite, even though logically you might think there are twice as many numbers between 0 and 2 that there are between 0 and 1. Infinite is a concept of "going on forever" and is not something that can be added to to or multiplied. But "goes on forever" so you can't really say there are more numbers between 0 and 2 than between 0 and 1. It is a hard concept to completely comprehend.įor instance, there are an infinite number of decimals between 0 and 1.Īnd there are an infinite number of decimals between 0 and 2.Īnd there are numbers between 0 and 2 that are not between 0 and 1. So there are lots (an infinite number) of both.Īnd saying one thing that is infinite is more than another infinite thing is questionable because you can't add to infinite. ![]() And there is at least one irrational number between any two rational numbers. Actually, Sal was saying that there are an infinite number of irrational numbers. ![]()
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