Fans of Buzz Lightyear know that his catchphrase is “To infinity…and beyond!” But is it even possible to go to infinity? Or beyond it? And exactly what is infinity, anyway?

If you think about a basic number line from your math class, you know that there’s no end to it. In both directions — positive and negative — it goes on forever. That “forever” is called infinity.

The concept of infinity is used mainly in the fields of mathematics and physics to refer to a quantity without end. In fact, infinity comes from the Latin word infinitas, which means “unboundedness.”

Mathematicians and physicists use a special symbol for infinity:∞. This symbol is sometimes called the lemniscate, which comes from the Latin word for “ribbon” (lemniscus).

John Wallis began using this symbol for infinity in 1655. Some believe he based it upon the Roman numeral for 1,000, which was often used simply to mean “many.” Others believe the symbol was based upon the last letter of the Greek alphabet: omega.

In mathematics, infinity has many applications. For example, the mathematical constant known as pi is an infinite decimal. But infinity is more than just a really large number.

Would you believe that there can be different sizes of infinity? It’s true! Consider this: there are an infinite number of positive whole numbers. There are also an infinite number of even positive whole numbers. Even though the number of positive whole numbers and even positive whole numbers are both infinite, the set of infinite positive whole numbers is twice as large as the set of infinite even positive whole numbers!

The concept of infinity is also popular with cosmologists who study the size of the universe. Does space simply go on and on forever without end? That is a question that remains unanswered. What scientists do know, though, leads many of them to believe that the universe may be infinite.

Beyond physics and mathematics, the concept of infinity can also have philosophical applications. For example, the infinite monkey theorem states that a monkey randomly hitting keys on a typewriter for an infinite amount of time will eventually type a given text, such as Moby Dick or the complete works of Shakespeare.

Some people use the infinite monkey theorem to suggest that, if given an infinite amount of time, anything is possible. Experts in statistics and probability, however, have shown that the theorem is actually better proof for how unlikely such events are. For example, the actual likelihood of a monkey exactly typing a complete work, such as Shakespeare’s Hamlet, is so tiny that, even given a period of time as long as the age of the universe, the probability is nearly zero!

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    • We’re glad you learned something new from this Wonder, Hayden! Thanks so much for visiting Wonderopolis today! :-)

    • That’s a GREAT question, Gage B, and it would make an AWESOME future Wonder of the Day®! Thanks so much for letting us know what you’re WONDERing about! :-)

  1. That is so cool! I want to make one of those! I always thought infinity was a number! Learn something new every day.

    • We’d love to see your Infinity Mirror if you make one, Jacob9! Thanks for letting us know how much you liked this Wonder! :-)

  2. HI,
    Could you please explain to me what the monkey theorem is? What the monkey theorem exactly says in philosophical view?

    • Hi, Amoolya! We think a scientist can best explain the infinite monkey theorem…we WONDER about it, too! Basically, some theorists believe that if someone (or some animal, like a monkey) is trying something (like hitting random keys on a keyboard) for a long enough amount of time (like infinity), that person or animal will EVENTUALLY be able to perform something amazing (like typing real words or a whole book). It’s like saying it might take a REALLY, REALLY long time, but if you try it, it will happen! Some other theorists, however, believe the exact opposite! :-)

  3. Hi! I heard the number pi and guess what! I know 17 numbers after the decimal of it! here it is
    3.14159265389575323… exc.. see!
    It is really hard for me to believe that infinity really exists. I can’t imagine it going on forever and ever. It is cool where the word comes from. I might be a little persnickety but I am very interested!

    Have people tried the experiment with the monkey? They maybe could do that because we share 97% of the same D.N.A. as them!
    Here is a fun fact! Did you know we are sort of canibals because we share about 8% of the same DNA as bananas!! We are part fruit!!

    ha ha ha!
    yours truly,
    Team Wilch #4

    • WOW, Team Wilch #4! Thanks for sharing all that AMAZING information with everyone in Wonderopolis! We didn’t know that we share some of the same DNA as monkeys and bananas! We like learning new things, too, so THANKS! :-)

  4. I had no idea the symbol for infinity was called lemniscate, meaning ribbon! Who knew that the infinite monkey theorom states that a monkey randomly hitting keys will eventually type up a text? I had no idea there were different sizes of infinity. Did John Wallis come up with the symbol for infinity, or was he just the first to start using it?
    – Team Unger 14

    • That’s a GREAT question, Team Unger 14! We’ll both have to do some more WONDERing to find out if Mr. Wallis created the lemniscate from either Roman numerals or Greek letters, or if it was a symbol that he just made up! We’re super glad you visited this Wonder! :-)

    • Hi, Ellen! We think it ROCKS that you shared this Wonder with your classmates! It’s so great that you guys are learning new things and WONDERing together! :-)

  5. This infinity thing is great, because I really enjoy watching illusions.
    Wonderopolis, you have the most interesting facts I have ever seen.
    Stay awesome!

    • What a SUPER nice comment you left for us, AwesomeMaster330! It makes us really happy to hear that you learn lots of interesting facts when you visit Wonderopolis! We promise to stay AWESOME if YOU will, too, OK? :-)

  6. Okay, I may have forgotten my last question. I was wondering how you find all of your videos for wonderopolis? Because I would really like to enter searches and see videos that you choose. I would also like to know if you have any youtube videos.

    • Thanks for leaving us another awesome comment, AwesomeMaster330! We search high and low for the best video to go along with each Wonder of the Day®! Sometimes we find the best video on YouTube, but sometimes it might be found on Vimeo or another video library website. We never know where we’ll find the perfect video for a Wonder of the Day®! :-)

      We’re working on new ways to be able to help our Wonder Friends (like YOU!) search for videos, links and activities here on Wonderopolis, so we appreciate you letting us know you’d like to search for Wonder videos. Thanks for being a GREAT Wonder Friend! :-)

  7. My dad told me that infinity is a number. It is the biggest number or the least number if negative infinity.

    • Thanks for sharing what your dad told you about infinity, Julie! We’re glad you stopped by Wonderopolis today! :-)

    • Thanks for leaving us this clever comment today, MickMuffin! You had us a little worried there for a minute, but we’re glad you thought this Wonder was really good! We WONDER if you know our Wonder Friend, Rithik? He’s REALLY awesome and we think he might be related to you! ;-)

    • Thanks for sharing your comment, Maddi! It makes us very happy to hear that a Wonder Friend has learned something new at Wonderopolis! Using your imagination is the best! Have a SUPER day! :)

  8. I loved this video because out of a few materials they made something awesome. I love Wonderopolis! I’m in Mrs. Atkinson’s class and I love checking the new Wonder every day with my class.

    • Hey Andrea, thanks for WONDERing with us today! We are so glad your class checks out the Wonders every day. Which one was your favorite from this past week? :)

    • Hi Third Grade Wonders! We’re so glad you’re WONDERing with us! We’ve had so much fun learning with you and think you’re AWESOME! Keep WONDERing! :)

  9. I wonder if infinity is an actual state ( which would of course operate on a different set of rules)Our universe has measurable dimensions its just that we don’t have the ability to measure it. Perhaps there are beings who live in and understand infinity. Sit down and think of infinity ( no beginning no end ) if you can UNDERSTAND that.Please post your understanding for me to learn.

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Have you ever wondered…

  • What is infinity?
  • What is the symbol for infinity?
  • What is the infinite monkey theorem?

Wonder Gallery

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Try It Out

We hope you’ve got a lot of extra time today, because you could spend an infinite amount of time exploring one or more of the following activities with a few friends or family members!

  • Does the concept of infinity blow your mind? If you have trouble imagining the size of an infinite universe, you’re not alone! It can be a challenge to understand the size of the universe when the world around us gives us few clues to the vastness of space. To get a better perspective of the size of the universe, click on over to Powers of Ten for a fun, interactive activity that will take you from a nap after a picnic lunch to the outer reaches of the universe!
  • If you’re still curious, check out the Hayden Planetarium’s Digital Universe Atlas online. You can also watch a neat video about The Known Universe created by the American Museum of Natural History! Does the vastness of space and the thought of an infinite universe boggle your mind? Does it make you feel small? Unique? Special? Discuss how you feel about infinity with a friend or family member.
  • Up for a challenge? If you want to make your own infinity symbol, watch this video to make your own Möbius strips! When you’re finished, learn more about these mathematical crafts by checking out this online Möbius Strip lesson.

Still Wondering

Check out Illuminations’ Making Your First Million lesson to learn to conceptualize very large numbers by first working with smaller numerical units.


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