# Mathematical Symbols and their Meanings?

Can someone give me some simple explanations of symbols used in maths such as !, ^, ∑, ∏, ∫, and any others that are important?

Thanks

Update:

I know what ! and ^ do now.

Relevance

! = factorial, hard to explain so i'll give an example.

5! is 5 x 4 x 3 x 2 x 1

8! is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

It gets more complicated if you're doing things like series but I'm assuming that if you don't know what it means you aren't interested in that.

^ is just a way to write something that would normally be superscript (like an exponent).

5^3 is five cubed

∑ = the greek letter sigma, which in math means summation, basically you do the sum of all numbers that meet a criterion that you specify.

∑(n=1,n=5) (5n) [I guess thats how you would write it in a computer] would be 5(1) + 5(2) + 5(3) + 5(4) + 5(5)

∏ = the greek letter pi, which in math is basically the same thing as the sigma except it's a product and not a sum.

∫ = integral, hard to explain if you've never taken calculus so accept this simple explination. If you had the equation y = x and you wanted to find the area under the line you would integrate x (it would look like ∫y = ∫xdx, sometimes you see ∫y as Y)

On that note, the opposite of this (which you should learn first actually) is the derivative. If we have y = x^2 than the derivative of this function will tell us what the slope is at any given point. It would look like this, dy/dx = 2x

as for others, there are a lot. A whole lot.

Just ones that I can think of off the top of my head:

epsilon(looks like an E): defines a set of numbers I believe (for every epsilon greater than zero there exists a delta greater than zero. . . [definition of a limit])

limit: the number that a graph converges to as you get arbitrarily close to a point from the left and from the right.

>, < = greater than, less than

log = again hard to explain so here is an example.

5^y = x

y = log(5)x

I was taught to think of it this way, y is the exponent i need to raise by base 5 to to get x as an answer.

ln = same as log except it is base e

e is just a constant like lower case pi.

sin, cos, tan, sec, csc, cot, and all of their inverse and hyperbolic functions = take a trig course.

that should be plenty to get you started.

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• ! means factorial. It is an operator which works on a single positive integer n, where n! = n * (n-1) * (n-2) .... * 2 * 1. In other words, n! is the product of all integers from 1 to n.

e.g. 4! = 4 * 3 * 2 * 1 = 24

5! = 5 * 4 * 3 * 2 * 1 = 120

100! = utterly huge

^ is a convenient way of writing 'to the power of' when you can't type those little super-script numbers,

e.g.

2^2 = 2 * 2 = 4

2^3 = 2*2*2 = 8

∑ means 'sum', or 'add together'

The ∑ symbol would often be written with little number above and below to indicate the limits of the summation.

e.g.

5

∑ n = 1+2+3+4+5 = 15

1

∫ has a similar meaning to ∑ except that all the things being added together are infinitesimally small. ∫ is used to indicate 'integration', a form of calculus, the reverse of differentiation.

∏ is a capital pi, but don't know what it's for.

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• Mathematical Symbols And Their Meaning

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• ! --> factorial, means that you multiply that number times all the numbers before it.

5! = 5 X 4 X 3 X 2 X 1

^ ---> raised to the power...

5^2 = 5 X 5

it is also a symbol to indicate the word 'and'

the next symbol is sigma. This symbol means the summation of whatever is inside

Sigma ( 5x) from x=1 to x=5 is 5+ 5(2) + 5(3) + 5(4) + 5(5)

the next symbol is pi. it is just a mathmatical constant (with infinintly many decimal places) that is rounded to about 3.1415. Very important when dealing with circles (for radians)

the final symbol is that for an integral, which is used in calculus. It is the anti-derivitive and is an operator for finding areas under curves, physics (velocity, position, acceleration), egineering (centers of mass, moments, dynamics, etc...), and many other high-level science classes such as physics.

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• They mean the following:

! - means factoral. It means that you multiply the given interger by all the lower integers. So: 5! = 5x4x3x2x1 = 120.

^ means 'to the power of. So 3^2 = 9.

∑ is sigma. It means sum. You apply it to a given function, so for example, you might have ∑1/x, for x = 1,2,3,4... etc..

It means add up 1/1 + 1/2 + 1/3 + 1/4 +1/5... (which diverges by the way and thus has no answer).

∏ means product. It's used like the sigma above. So ∏ 1/x, for x = 1,2,3,4 etc means 1/1 x 1/2 x 1/3 x 1/4 x...

Finally, ∫means integrate. Geometrically, it means find the area under a curve defined by the given function. I don't want to go into how you actually do this - you'll need to take a course in calculus to find out!

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• Anonymous

! means multiply each number in its decreasing sequence

for example

6! = 6 x 5 x 4 x 3 x 2 x 1

6! = 720

^ means to raise to the power of

so for ex.

x^2 = x sqaured

or

3^2 = 3 squared = 9

the third symbol is the summation symbol look it up its hard to explain

the fourth is also some type of summation but not really

the fifth is something used alot in calculus

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• Do you know that * sign means multiplication? 3*4 = 3x4 = 12

!:

1! = 1;

2! = 1*2;

3! = 1*2*3;

4! = 1*2*3*4;

.....

n! = 1*2*3* .... *(n-1)*n

Also, 0! = 1

^: to the power

4^2 = 16; 5^3 = 125 and so on

4^(-2) = 1/16; 5^(-3) = 1/125

∑: summation sign

n

∑r : means summation over r from 1 to n

1

n

∑r = 1 + 2 + 3 + ..... + n

1

n

∑r^2 = 1^2 + 2^2 + 3^2 + ..... + n^2

1

∏: multiplication symbol

n

∏ (r - 2) = 1*2*3* ..... *(n - 3)*(n - 2)

3

∫: integration symbol

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• ! is factorial. (Many have explained it to you.)

^ is exponentiation. a^b means a raised to power b.

∑ is summation. It means adding the respective terms

∑ i where i runs from 1 to 5 means 1+2+3+4+5

∏ is pi product. This time it means multiplying respectively.

∑ i where i runs from 1 to 5 means 1*2*3*4*5

∫ is the sigma notation for integration. It is needed in calculus.

D is for the derivative. This is the inverse operation of integration.

Edit:

trivia note: 0! = 1 (by special definition.)

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The mathematical symbol for infinity is known as the lemniscate. It was devised in 1655 by mathemetician John Wallis, and named lemniscus, ribbon, by Bernoulli about forty years later. The symbol is patterned after the device known as a mobius (named after a nineteenth century mathemetician) strip. A mobius strip is a strip of paper which is twisted and attached at the ends, forming a two dimensional surface. The religious aspect of the infinity symbol predates its mathematical origins. It has been found in Tibetan rock carvings; the ouroboros, or infinity snake, is often depicted in this shape. In the tarot, the lemniscate represents the balance of forces and is often associated with the magician card.

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• The third in your list is a capital sigma (Greek), and designates summation; a range of values is often specified along with the function f(x) whose values in the range are being summed.

The fourth symbol is a capital pi (Greek). Same idea as the sigma but a product (multiplication) rather than sum.

The last is the integral sign in calculus. I'd suggest going to wikipedia or other reference to get an idea of the background if your not conversant with calculus.

Many lower case Greek letters are used in statistics and other branches of math, and of course lower case pi is the ratio of the circumference of a circle to its diameter.

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