And the sequence x 1, x 2, … x 3 implies the same. The possibility of its indefinite continuation, and no more-certainly notįor example, the numbers 1, 2, 3, … imply that you can keep on counting forever, without reaching an end. “The infinitude of a process, collection, or magnitude was understood as Stillwell describes how most mathematicians didn’t warm to the concept of infinity until well after the 19th century. In his book, Mathematics and Its History, J. This represents the cardinality of the infinite set of natural numbers- the number of elements in that set. The first transfinite cardinal number is written as Ν 0, which we read as Aleph-naught. The infinite (transfinite) numbers each have their own designation. The Peano axioms, for instance, the basic rules which guide the way we add, subtract, and understand real numbers, do not apply in any way to the transfinites. So, if a number falls into the “transfinite infinity” class, then yes- it’s a number.Īlthough infinite numbers- i.e, the transfinites- are sometimes called numbers, it’s important to realize this does not mean they are natural numbers, real numbers, or any other type of number that we are used to working with and manipulating. More properly, these are called transfinite numbers. Is Infinity a Number if It’s Transfinite?Īlthough infinity is not a number, there are a special class of numbers sometimes referred to as “infinite numbers” which are bigger than all finite numbers. Set theory is beyond the scope of this article but if you’re interested in reading more on countable and uncountable sets, read Countable and Uncountable Sets.
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Uncountable infinity is where the set contains all the numbers and everything in between, like 1, 1.22, 1.23, 1.256…. Countable infinity is when it’s easy to label the numbers (like if you’re counting whole numbers 1, 2, 3…. In set theory, things get a little more complicated, because sets can have countable infinity, or uncountable infinity. For example, if you’re looking at a number line, positive infinity is the last possible “number” to the left negative infinity is always the last possible “number” to the far right. Which exact definition you use depends on which specific area of math you’re working with.
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That isn’t quite correct, but it’s good enough for most purposes. If Infinity it isn’t a number, what is it?Ī common definition for infinity is that it’s a quantity bigger than any number. That’s what the concept of infinity means- something without bound, larger than any natural numbers. An easy way to associate this mentally with the concept of infinity is to realize that you can travel endlessly around the curve- there is no beginning and no end. The infinity symbol (∞) is a lazy eight curve- an eight lying on its side (not to be confused with “the” eight curve). Infinity is a concept, an idea that is related to numbers and counting systems but it is not a number. Is infinity a number? The simple answer is no. Feel like "cheating" at Calculus? Check out our Practically Cheating Calculus Handbook, which gives you hundreds of easy-to-follow answers in a convenient e-book.