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Is 1 infinity possible?

Infinity is a concept, not a number. We know we can approach infinity if we count higher and higher, but we can never actually reach it. As such, the expression 1/infinity is actually undefined.

study.com - Solving 1 Divided by Infinity - Video & Lesson Transcript - Study.com

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Limit of a Function

Let's use the following table to take a look at the value of 1/x for the values of x as they approach infinity.

x 1/x 1 1 10 0.1 1,000 0.001 1,000,000 0.000001 1,000,000,000 0.000000001

In mathematics, a limit of a function occurs when x gets larger and larger as it approaches infinity, and 1/x gets smaller and smaller as it approaches zero. As we can't find a value for 1/infinity, the limit of 1/x as x approaches infinity is as good as we're going to get. In general, the limit of a function tells us what value the function approaches as x approaches a certain value. We can use the following notation for the limit of f(x) as x approaches a. In this instance, we're taking the limit of the function 1/x, and x is approaching infinity. According to our table, the limit of 1/x, as x approaches infinity, is 0.

Graphs & Limits

In finding the limit of 1/x as x approaches infinity, we used a table of values to observe a pattern to evaluate the limit. This can also be observed graphically. On graphs, limits as x approaches infinity or negative infinity show up as horizontal asymptotes. An asymptote is a line that a graph approaches, but does not touch. Consider our example. We found that the limit of 1/x as x approaches infinity is 0. Graphically speaking, this says that if we look at the graph of y = 1/x, we'll see that as x gets larger and larger, or the further we go along the x-axis to the right, the closer the graph will get to the line y = 0. However, since we can't actually reach infinity to evaluate 1 divided by infinity, the graph won't ever actually reach the line y = 0. Instead, it will just approach it.

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