# Why does zero factorial is equal to one?

n! = n * (n-1) ! Interchange LHS and RHS n * (n 1) ! = n! (n-1) ! = n! /n substituting n = 1 (1-1)! = 1! / 1 0! = 1 / 1 = 1 A: By Ducnhuando…an Onother proof is: A Schema Proof Without Words That Zero Factorial Is Equal To One. 6! = 720 = 1*76 -6*66 +15*56 -20*46 +15*36 -6*26 +1*16. 5! = 120 = 1*65 -5*55 +10*45 -10*35 + 5*25 -1*15. 4! = ..24 = 1*54 -4*44 + 6*34 - 4*24 + 1*14. 3! = ....6 = 1*43 -3*33 + 3*23 - 1*13. 2! = ....2 = 1*32 -2*22 + 1*12. 1! = ....1 = 1*21 -1*11. 0! = … ..= 1*10. 0! =... ....= 1*10 = 1*1 = 1. Conclusion 0!=1 The proof "without words" above that zero factorial is equal to one is a New that: *One has not to accept by convention 0!=1 anymore. *Zero factorial is not an empty product. *This Schema leads to a Law of Factorial. Invention's Author: Ducnhuandoan (Đoàn Đức Nhuận by vietnamese) By clicking Ducnhuandoan or LawsfromABCMaths on any searching tool on internet you can see more about my easymath.

# Prove that one equals zero?

"Proof" that 1 = 0. Postulates: We know that one third = 1/3 which in decimals is written 0.3333... ("..." will represent recurring decimals) We also know that thr…ee thirds = 3/3 which is a whole, i.e. 1. Corollary: So 1 - 3/3 = 0 by definition. This implies that 1 - (3 x 0.3333...) = 0 Tricky: But multiply 0.3333... by 3 and you get 0.9999... (You can check this by multiplying each decimal by 3. Since none of them will exceed 10 {as 3x3=9}, each can be calculated separately and then strung back together) Following the reasoning above, 1 - 0.9999... = 0 Which you can rearrange to get 1 = 0.9999... So subtract 1 from both sides, you get that 0.0000...0001 = 0 Divide both sides by 10 infinitely* repeatedly until all the decimal zeroes are removed and you get 1 = 0. NOTE: This is a common [[fallacy]] in the transformation between fractions and decimals which often misguides students into making false assumptions (similar to saying that 1 divided by 0 is infinity "because 0 goes into 1 infinite times"). *The fact that we had to use infinity at all to prove this (divide by 10 infinitely) should alert the student that even the most basic presumptions have to be reviewed (see note).

# Why zero factorial is equal to one?

n factorial is defined as: n! = n x (n-1) x (n-2) ... x 1 So, n! = n x (n-1)! If we replace "n" with 1: 1! = 1 x 0! … 1 = 1 x 0! 1 = 0! so, 0! is equal to 1. Why Zero Factorial is Equal to One Why should you be concerned that 0!=1? You may not even know what a factorial number is. Reading the following you may come to understand the idea of a factorial.You may also be able to please your friends and confound your enemies bybeing able to show that 0!=1. Here is an explanation, requiring only knowledge of simple arithmetic tounderstand. When considering the numbers of different groups which may be formed from acollection of objects one frequently finds the need to make calculations ofthe form, 4 x 3 x 2 x 1 for 4 objects. I suppose I must explain why that is. Say we have the four objects A, B, C, D. If I select from that collection to form another group, you will see that Icould choose any one of the four for the first selection. Thiswould leave three objects. I could select any of those three for the second selection,leaving any one of two for the next and so on. The total number of ways I could selectthose objects would be 4 x 3 x 2 x ... , and the series would stop at one when I selectedthe last object. To save repeatedly writing down long strings of such products thenotation 4! is used to represent 4 x 3 x 2 x 1 or 6! for 6 x 5 x 4 x 3 x 2 x 1.The ! is read as factorial. So the examples quoted above are more easily written as 4!and 6!. If you care to calculate their values they are 24 and 720 respectively. In general any factorial number (call it n!), may be written, n! = n x (n-1) x (n-2) x (n-3) x ... x 2 x 1 This is the general definition of a factorial number. If you want it in words; a factorial number is the product of all positive integers from1 to the number under consideration. The main place it is likely to be encountered is when considering those groups andarrangements of objects mentioned above. So where does all this 0! stuff fit in? Nobody has trouble in stating 2! = 2 x 1 , or even that 1! = 1, but 0! appears to make nosense. It does however, have a value of 1. This is rather counter intuitive but arisesdirectly from our general definition. n! = n x (n-1) x (n-2) x (n-3) x ... x 2 x 1 Notice this may be written, n! = n x (n-1)! Still exactly the same definition. If the left hand side (LHS) = the right hand side (RHS) then dividing both sides by nshould leave them still equal, so it is still true to write, n!/n = n x (n-1)!/n The (n-1)! in the RHS is being both multiplied by n and divided by n. These cancelleaving, n!/n = (n-1)! If you doubt this, try it with real numbers, e.g. 4!/4 = 3! or (4 x 3 x 2 x 1)/4 = 3 x 2 x 1 = 6 The equation we now have is, n!/n = (n-1)! It is still our original definition in arearranged form. For convenience I shall write it the other way round. (n-1)! = n!/n We also said that our factorial uses the positive integers 1 and above.Try the value of n=2 in our rearranged formula and we get, (2-1)! = 2!/2 or 1! = 2x1/2 The RHS calculates to 1, so we have the statement 1!=1That is what we guessed intuitively above. It is now confirmed.But look what happens when we substitute the legitimate value of n=1 in our formula. (1-1)! = 1!/1 Evaluating this statement gives 0! = 1!/1 We have just shown 1!=1 so the RHS is 1/1 or 1. Our rearranged definition of a factorial number gives directly the statement, 0!=1 Counter intuitive perhaps but if the definition is true then this is true. Why not tell your friends about it? Help dispel the widespread ignorance about 0!

# How do you solve zero is equal to one?

0 = 1 is incorrect

# Why number raise to zero equals to one?

The simplest way to understand this is to consider what happens to powers of numbers as the exponent is increased or decreased. If you take any number, call it "X" and r…aise it to a power, let's use 4 as an example, you express it as X4. Consider what would lower that number by 1, giving you X3. For it to become X3, you would simply divide X4 by X. In other words: X3 = X4 / X or more generically, Xn / X = X(n - 1) So what happens if you logically follow that pattern down to the smallest value of n? Well, consider our example: X4 / X = X3 X3 / X = X2 X2 / X = X1 X1 / X = X0 X1 is equal to X, no matter what the value of X is. This means that according to our last statement, X0 = X / X. Of course X / X is always equal to one, as long as X is not equal to 0. That means that X0 must equal 1 as well, for any non-zero value. 00 is the one exception here, as that value is undefined. The reason for this is clear if you consider what it means. As stated above, X0 is equal to X / X. In the case of X = 0 though, that would mean it's equal to 0 / 0. That value is undefined, and therefore 00 is as well.

# Why one factorial and zero factorial is same?

As we know product of no numbers at all is 1 and for this reason factorial of zero =1 and we know factorial of 1=1

# Zero factorial equal to one factorial then if we cancel the factorials on both side then the answer becomes zero equals one. do u accepts this?

0!=1! 1=1 The factorial of 0 is 1, not 0

# Why is a number raise to zero is equal to one?

x to the n divided by x to the n is 1. By the law of powers x to the power n divided by x to the power n is x to the power (n minus n), ie x to the power zero. Things whic…h are equal to the same thing are equal to each other. Therefore x to the power zero = 1. (Unless x = zero!)

# Why everything to power of zero is equal to one?

x to the power a divided by x to the power b is x to the power (a - b) When a and b are equal then this is x to the power a divided by x to the power a, ie 1. x to the power (…a - a) = x to the power zero. Things which are equal to the same thing are equal to each other, so 1 = x to the power zero.

# What symbol equals zero point zero one meter?

1 cm or one centimeter.

# Why does zero equal one?

Zero is not equal to one. However, they have a similarity; each one is an identity element in our standard arithmetic (z is an identity element if a*z = a for some operation *…). Here, a+0 = a a*1 = a

# Why a number when it is to the power of zero is equal to one?

Let any number be n:- n3/n3 = n*n*n/n*n*n = 1 And in index form: n3/n3 = n3-3 = n0 = 1

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In Numbers

# Why exponent zero on a number is equal to one?

The simple way to reason it is this: think backwards. Say I tell you that 210=1024. Given this how would you find 29? You would never want to multiply the whole thing out agai…n. You would probably divide 210 by 2. What's 23? 8. What is 22? divide that last answer by 2 to get 8/2 = 4. What is 21? divide the last answer by 2 to get 4/2 = 2. What is 20? divide the last answer by 2 to get 2/1 = 1. In higher mathematics, the reason comes from the definition. Mathematicians define a0 = 1 and then they define an+1 as an * a. Let me think of an example. If we define 20=1, then what is 21? 21= 20+1= 20*2 (this is because we defined it this way an*a = an+1). = 1*2 = 2. We can similarly define every exponent in this way by using the one below it. Mathematicians call this a definition by induction.

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In Algebra

# Why does one to the power of zero equal zero?

Any number to the power zero equals 1. A possible exception is zero to the power zero. Some people claim it is equal to zero, others say it equals one, consistent with any ot…her value. Still more say that the result of zero to the power zero is an undefined value. With the possible exception of zero, the statement above holds true for any value.

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In Algebra

# Why does everything to the zero power equal one?

The easiest way to see this is to consider what happens when you have a base raised to an exponent and divide it by that base. Consider: x10 / x = x9 x9 / x = x8 Or more g…enerically: xn / x = xn - 1 Logically then, we can extend this all the way down to one: x1 / x = x0 And what is x1 / x? That's simply x/x of course, so we have: x0 = x/x x0 = 1 So with the exception of zero, anything to the power of zero is equal to one. A base of zero is an exception here. Using the same logic consider what it would mean: 00 = 01/0 That would give us zero divided by zero, which is undefined, hence the 00 being undefined as well.

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In Proofs

# Why does zero power is equal to one?

To divide a number raised to one power by the same number raised to a nother power, you subtract the powers; eg 5 cubed divided by 5 squared is 5 to the power (3 - 2) ie 5. If… you divide 5 cubed by 5 cubed then you have 5 to the power (3 - 3) ie 0, but 5 cubed divided by 5 cubed is 1 hence 5 to the power zero is one. This calculation holds good for any non-zero number. If you are satisfied with this reply please consider awarding a Recommended Point to the responder.

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# Why does two to the zero power equal one?

According to the rules of exponents, n x /n y = n x-y . For example, 2 2 /2 2 = 4/4 = 1. Subtracting the exponents gives 2 2-2 = 2 0 . Therefore, 2 0 = 1.