10 Facts that you don't know about the infinity symbol

The existence of an infinite set is an assumption of modern mathematics, in that you can't start with finite sets, together with the standard set operations , and actually construct an infinite set. Many mathematicians take this as a reason to reject any form of math which depends on infinite sets.

10. The Infinity Symbol

The infinity symbol is also known as the lemniscate.
Infinity has its 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."
Various theories are propounded for infinity like Ancient cultures had various ideas about the nature of infinity. They did not describe it as a symbol like in mathematics but explained it as a philosophical concept.

10.1. In mathematics, Calculus, Leibniz speculated infinite numbers and their use in mathematics.
In Real analysis also the symbol infinity is used to denote an unbounded limit.
Even in Complex analysis, the symbol infinity denotes an unsigned infinite limit etc.

10.2. Infinity - the doctrine of Bhuma
The drift of the statement is that infinity is unchanging and this mantra is a figurative way of saying that nothing proceeds from infinity. Even the idea of something proceeding from infinity is based on its essential character of infinity.

9. Infinity Minus Infinity Does Not Equal Zero

Infinity minus infinity is undefined in the same way that dividing by zero is undefined. To give an example of why this is, since infinity plus one equals infinity ([infinity + 1] = [infinity]), if we subtract infinity from both sides, we are left with 1 = 0. Similarly, and for many of the same reasons, infinity divided by infinity is not one but is also undefined.

8. Some Infinities Are Bigger Than Others

The flip side of the one-to-one correspondence is that if there is an infinite series of numbers that still have numbers left over after being matched up with another infinite series, then we can say that the former series of infinities is larger than the infinity that it was matched with. This might seem impossible, but you can probably intuitively grasp a case where this is true: the infinite number of whole numbers (0, 1, 2, 3 . . . ) is smaller than the infinite number of irrational numbers. If you recall from high school math, irrational numbers are numbers like pi that have a series of decimals that go on forever (3.1415 . . . ). Cantor showed that the infinite number of irrational numbers is larger than the infinite number of whole numbers using an ingenious but simple (relative to most groundbreaking mathematical proofs) trick. He began by assuming that irrational numbers could be matched up with whole numbers and wrote down a series of numbers between zero and one. (Okay, these are my random numbers from mashing the keyboard, but you get the point.) There is an infinite number of these rows:0.1435 . . . matched with 0
0.7683 . . . matched with 1
0.1982 . . . matched with 2
0.9837 . . . matched with 3 and so on. You can then create a number from this series by taking the first digit in the first line, the second digit in the second line, and so on; for the numbers above, this would be 0.1687...Now, there might be a number of 0.1687 . . . somewhere in this stack of numbers. However, if you add one to each of the digits, then the number becomes 0.2798 . . . , and this number cannot be in the stack since it is by definition different from any of the numbers in the stack by at least one digit. Therefore, there are still irrational numbers left over after trying to match them up with normal whole numbers. Therefore, we can say that the infinite number of irrational numbers is larger than the infinite number of whole numbers.

7. Zeno's Paradox

A day has only a finite number of hours and a finite number of minutes, but you do infinitely many things every day. Even just to walk over to the fridge you cover an infinite number of distances: first, you have to cover half the distance, then half the remaining distance, and half the remaining distance, and so on forever.
Fortunately, you can cover those infinitely many distances infinite time, otherwise, you’d be infinitely hungry. This is Zeno’s paradox and wasn’t resolved until the invention of calculus a couple of thousand years after Zeno died.

6. Pi as an Example of Infinity

A pi is a number consisting of an infinite number of digits.
Another good example of infinity is the number of 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.

5. The Monkey Theorem

Given an infinite amount of time, a monkey could write the great American novel.
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. Fractals and Infinity

A fractal may be magnified over and over, to infinity, always revealing more detail.
A fractal is an abstract mathematical object, used in art and to simulate natural phenomena. Written as a mathematical equation, most fractals are nowhere differentiable. When viewing an image of a fractal, this means you could zoom in and see new detail. In other words, a fractal is infinitely magnifiable.
The Koch snowflake is an interesting example of a fractal. The snowflake starts as an equilateral triangle. For each iteration of the fractal:
Each line segment is divided into three equal segments.
An equilateral triangle is drawn using the middle segment as its base, pointing outward.
The line segment serving as the base of the triangle is removed.
The process may be repeated an infinite number of times. The resulting snowflake has a finite area, yet it is bounded by an infinitely long line.

3. Different Sizes of Infinity

Infinity comes in different sizes.
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 > ∞.

2. Cosmology and Infinity

Even if the universe is finite, it might be one of an infinite number of "bubbles.".
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 one in an infinite number of them.

1. Dividing by Zero

Dividing by zero will give you an error on your calculator.
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 the math.