In terms of cardinal numbers you can't count past infinity. There are of course infinite sets with larger cardinality than the natural numbers, for example the real numbers. Is there a number before infinity? There isn't a number before infinity because there isn't a number called infinity.
Therefore, 0 is the smallest one - digit whole number and 1 is the smallest- one - digit natural number. In the decimal number system, the smallest one digit number is 1. Therefore to answer the question, how many one digit numbers are there, there are ten one digit numbers including 0. The number 1 happens to be its own multiplicative inverse. No other positive integer has a multiplicative inverse within the set of integers. The number - 1 is also a unit within the set of integers: again, it is its own multiplicative inverse.
The first recorded zero appeared in Mesopotamia around 3 B. The Mayans invented it independently circa 4 A. Or the digits of pi after the decimal — do they actually run on endlessly, always giving us that much more precision about the ratio between a circle's circumference and radius?
And, could Buzz be right? Is there something beyond infinity? In order to tackle these mind-bending speculations, Live Science enlisted the help of mathematician Henry Towsner from the University of Pennsylvania in Philadelphia, who was kind enough to try answering the question, "Can you count past infinity?
Related: Image Album: Visualizations of Infinity. Infinity, Towsner said, sits at a strange place: Most people feel like they have some intuition about the concept, but the more they think about it, the weirder it gets. Mathematicians, on the other hand, don't often think of infinity as a concept on its own, he added.
Rather, they employ different ways to think about it in order to get at its many aspects. For instance, there are different sizes of infinity. This was proven by German mathematician Georg Cantor in the late s, according to a history from the University of St Andrews in Scotland. Cantor knew that the natural numbers — that is, whole, positive numbers like 1, 4, 27, 56 and 15, — go on forever. They are infinite, and they are also what we use to count things, so he defined them as being "countably infinite," according to a helpful site on history, math and other topics from educational cartoonist Charles Fisher Cooper.
Groups of countably infinite numbers have some interesting properties. For instance, the even numbers 2, 4, 6, etc. Suppose you count the first ten numbers at a slow pace, but with every subsequent 10 numbers you count twice as fast, then he proves that you will reach infinity in a finite time.
But that requires you to eventually count infinitely fast. Some primitive languages have words for one, two and three, but everything beyond is "many".
However these people can still work out whether a set with more than three elements is bigger or smaller than another set. The method is pairing the elements one by one and the bigger set will have elements that cannot be paired with elements of the smaller set. This pairing idea is used in the metaphor of the Hilbert hotel to illustrate that there are as many rational numbers as natural numbers.
Then Du Sautoy illustrates that people needed irrational numbers like for example the square root of 2 and pi. With Cantor's diagonal principle he can illustrate that there are more irrational numbers than rationals. And there we are: we reached infinity and even went beyond to a next level. Du Sautoy concludes: "The trick was not to start counting, '1,2,3,' and then to hope to reach infinity. Instead, a change of perspective allowed us to think of infinity in one go and, by doing so, to show that infinity is a many-headed beast.
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