As you might well expect, I am a huge fan of the Toy Story movie franchise. I think Buzz Lightyear is out of this world. (Yep, pun intended.) One of Buzz's most famous lines is, "To infinity and beyond!" You don't need to be a math geek to be intrigued by infinity. It kind of hurts my little froggy brain to think about it for too long, yet I do find it fascinating. Today, I have for you a few infinity facts that will, I think, blow your mind...but in a really fun and good way.
Infinity is an abstract concept used to describe something endless or boundless. It is important in mathematics, cosmology, physics, computing, and the arts. "Infinity has a special symbol: ∞. The symbol, sometimes called the lemniscate, was introduced by clergyman and mathematician John Wallis in 1655. The word "lemniscate" comes from the Latin word lemniscus, which means "ribbon," while the word 'infinity' comes from the Latin word infinitas, which means boundless."
Ready for a few mind-altering facts about infinity? Here we go!
1. The Infinity Symbol. The concept of infinity was understood long before Wallis gave it the symbol we use today. Around the 4th or 3rd century B.C.E., the Jain mathematical text Surya Prajnapti assigned numbers as either enumerable, innumerable, or infinite. The Greek philosopher Anaximander used the work apeiron to refer to the infinite. Zeno of Elea (born circa 490 B.C.E.) was known for paradoxes involving infinity.
2. Pi as an Example of Infinity. A good example of infinity is the number π or pi. Mathematicians use a symbol for pi because it's impossible to write the number down. Pi consists of an infinite number of digits. It's often rounded to 3.14 or even 3.14159, yet no matter how many digits you write, it's impossible to get to the end.
3. The Monkey Theorem. One way to think about infinity is in terms of the monkey theorem. According to the theorem, if you give a monkey a typewriter and an infinite amount of time, eventually it will write Shakespeare's Hamlet. While some people take the theorem to suggest anything is possible, mathematicians see it as evidence of just how improbable certain events are.
4. Different sizes of Infinity. Who knew it came in small, medium, and large? Infinity is boundless, yet it comes in different sizes. The positive numbers (those greater than 0) and the negative numbers (those smaller than 0) may be considered to be infinite sets of equal sizes. Yet, what happens if you combine both sets? You get a set twice as large. As another example, consider all of the even numbers (an infinite set). This represents an infinity half the size of all of the whole numbers. Another example is simply adding 1 to infinity. The number ∞ + 1 > ∞. Your head hurt yet? Not to worry. I'm almost done.
5. Cosmology and Infinity. Cosmologists study the universe and ponder infinity. Does space go on and on without end? This remains an open question. Even if the physical universe as we know it has a boundary, there is still the multiverse theory to consider. That is, our universe may be but one in an infinite number of them. And, finally...
6. Dividing By Zero. Dividing by zero is a no-no in ordinary mathematics. In the usual scheme of things, the number 1 divided by 0 cannot be defined. It's infinity. It's an error code. However, this isn't always the case. In extended complex number theory, 1/0 is defined to be a form of infinity that doesn't automatically collapse. In other words, there's more than one way to do math.
Okay, I officially have a headache now. But you have to admit, these facts are kind of fun! If you know a math geek, you might want to shares this with them. They'' be happy you did. And who knows? You may get a few extra brownie points!
I try to write about a variety of subjects, some that I know will be more popular than others. But learning new things and sharing them with you, my readers will, hopefully help us both to grow and expand our way of looking at the world.
Tomorrow is Wednesday and that means Dharma Frog will be here for my weekly life lesson. You can bet that it'll be helpful and not nearly as dry or mild-altering as these facts about infinity. If you've managed to hang in there this long, I truly appreciate it! Until we meet again, I wish you a TOAD-ally awesome Tuesday.
PEACE.
Infinity is an abstract concept used to describe something endless or boundless. It is important in mathematics, cosmology, physics, computing, and the arts. "Infinity has a special symbol: ∞. The symbol, sometimes called the lemniscate, was introduced by clergyman and mathematician John Wallis in 1655. The word "lemniscate" comes from the Latin word lemniscus, which means "ribbon," while the word 'infinity' comes from the Latin word infinitas, which means boundless."
Ready for a few mind-altering facts about infinity? Here we go!
1. The Infinity Symbol. The concept of infinity was understood long before Wallis gave it the symbol we use today. Around the 4th or 3rd century B.C.E., the Jain mathematical text Surya Prajnapti assigned numbers as either enumerable, innumerable, or infinite. The Greek philosopher Anaximander used the work apeiron to refer to the infinite. Zeno of Elea (born circa 490 B.C.E.) was known for paradoxes involving infinity.
2. Pi as an Example of Infinity. A good example of infinity is the number π or pi. Mathematicians use a symbol for pi because it's impossible to write the number down. Pi consists of an infinite number of digits. It's often rounded to 3.14 or even 3.14159, yet no matter how many digits you write, it's impossible to get to the end.
3. The Monkey Theorem. One way to think about infinity is in terms of the monkey theorem. According to the theorem, if you give a monkey a typewriter and an infinite amount of time, eventually it will write Shakespeare's Hamlet. While some people take the theorem to suggest anything is possible, mathematicians see it as evidence of just how improbable certain events are.
4. Different sizes of Infinity. Who knew it came in small, medium, and large? Infinity is boundless, yet it comes in different sizes. The positive numbers (those greater than 0) and the negative numbers (those smaller than 0) may be considered to be infinite sets of equal sizes. Yet, what happens if you combine both sets? You get a set twice as large. As another example, consider all of the even numbers (an infinite set). This represents an infinity half the size of all of the whole numbers. Another example is simply adding 1 to infinity. The number ∞ + 1 > ∞. Your head hurt yet? Not to worry. I'm almost done.
5. Cosmology and Infinity. Cosmologists study the universe and ponder infinity. Does space go on and on without end? This remains an open question. Even if the physical universe as we know it has a boundary, there is still the multiverse theory to consider. That is, our universe may be but one in an infinite number of them. And, finally...
6. Dividing By Zero. Dividing by zero is a no-no in ordinary mathematics. In the usual scheme of things, the number 1 divided by 0 cannot be defined. It's infinity. It's an error code. However, this isn't always the case. In extended complex number theory, 1/0 is defined to be a form of infinity that doesn't automatically collapse. In other words, there's more than one way to do math.
Okay, I officially have a headache now. But you have to admit, these facts are kind of fun! If you know a math geek, you might want to shares this with them. They'' be happy you did. And who knows? You may get a few extra brownie points!
I try to write about a variety of subjects, some that I know will be more popular than others. But learning new things and sharing them with you, my readers will, hopefully help us both to grow and expand our way of looking at the world.
Tomorrow is Wednesday and that means Dharma Frog will be here for my weekly life lesson. You can bet that it'll be helpful and not nearly as dry or mild-altering as these facts about infinity. If you've managed to hang in there this long, I truly appreciate it! Until we meet again, I wish you a TOAD-ally awesome Tuesday.
PEACE.
Helmenstine, Anne Marie, Ph.D. "8 Infinity Facts That Will Blow Your Mind." ThoughtCo, Oct. 19, 2018, thoughtco.com/infinity-facts-that-will-blow-your-mind-4154547.
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