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Infinity is a concept that challenges the limits of human comprehension. The idea of something that is endless or never-ending is hard to grasp because our experiences and perceptions are bound by finite boundaries. However, despite its abstract nature, infinity has a critical role in mathematics, where it is used to describe unbounded values, limits, and sets.

What is infinity?

Infinity is not a number, and it cannot be measured. But we do see the concept of infinity popping up in math all the time. Try dividing 10 into three equal part the resulting decimal has an infinite number of "3"s trailing off forever. If we punch this equation into our calculator, we would get 1.33.. and our entire screen would be filled with 3s.

This is one example of infinity in math.

Other examples include the golden ratio, which is 1.618..

In math, we use ".." to show that these numbers are trailing off, and that they have no end.

You might also see infinity represented by the symbol "∞."

This symbol was crafted by the mathematician John Wallis, who was inspired by the Möbius strip -- a 3d shape that has one side by looping back to itself.
Infinity is a fascinating concept that goes beyond our everyday experience of numbers and measurement. It is a tool that helps us to explore the endless possibilities of mathematics and the universe around us. Infinity is essential in calculus, where we study the behavior of functions and their limits as they approach infinity. It is also used in geometry, where we examine the properties of curves and shapes that extend to infinity.
For example, if we take the function

f(x) = 1/x
and evaluate it as x approaches infinity:

lim f(x) = 0x → ∞
f(1) = 1

and so on, for no real value of x does the function actually equal zero, but we can get as close to zero as we like with a choice of our x value.

Topics related to the Infinity

Infinite Geometric Series


End Behavior of a Function

Flashcards covering the Infinity

Calculus 1 Flashcards

AP Calculus AB Flashcards

Practice tests covering the Infinity

Calculus 1 Diagnostic Tests

AP Calculus BC Diagnostic Tests

Help your student gain confidence in math class

The concept of infinity is sometimes hard to grasp, especially when trying to think of practical applications that use it. Working with a private tutor gives your student the individualized help they need to understand abstract math concepts like infinity. Help your student reach for their mathematical dreams by contacting Varsity Tutors today.

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