It is correct that 1!=0!; so 1=0; where is the falacy?

Answer 1

The factorial function satisfies 1!=1 and 0!=1. The trouble is you're trying to take the "inverse factorial function" of 1, which you cannot do because the factorial function is many-to-one function.

Another example: Consider the function f(x)=x(x-1). It is clear that f(0)=0=f(1). Does this imply that 0=1? Of course not.

Answer 2

(-2)^2 = (2)^2; so -2 = 2

Let's pretend that the # sign undoes factorials. So 1! = 0! could be solved by # on both sides #(1!) = #(0!). If we applied the #, to a 1 it would result in either a 0 or 1. So 1 or 0 = 1 or 0.

This is simular to how sqrt(4) = -2 or 2

Answer 3

Your calculator rounds to the nearest valid whole number that can be 'factorialed'
3! = 6
4! = 24
3.5! = 24
3.499! = 6
0! = 1 (zero gets rounded up to 1)
-137,568,273! = 1 (again rounded up to 1)
By definition of the function you can only factorial positive whole numbers. 0 is not a positive whole number.
It can be true that if f(x) = f(y) then x = y when every value of x represents a unique value for f(x).

Note for insideoutstock since your e-mail is not confirmed by yahoo

hmmm.
I suppose it is true that the way the function behaves is as you state where x!=x(x-1)! in general, however the special case where x = 0 is revealing the limitation of the calculator being used showing the simplification method that's built in to the calculator's processor.
The definition of factorial IS the product of all positive integers starting from one to a given whole number being factorialed. By definition 0 is not an allowable number for the function.

Answer 4

0! is a special case and is defined as 1, as in "there is 1 way to arrange zero objects". It's a convention. There is no unique inverse for the factorial function. Similarly, you cannot say that 2*pi = 0 because sin(2*pi) = sin(0).

Answer 5

1! is 1 so is 0! because ! mean a number multiplied by its smaller number and so on like 5! is 120 and 1 is just left by itself and zero can't be multiplied by anything since its only one thing but 1 may not equal to 0 in the second part

Answer 6

The gamma function (factorials for integers) is not a one-to-one function. That is, there exists x and y not equal to each other such that f(x) = f(y). That's the case with factorials and 0 and 1. The fallacy is assuming that the function is a one-to-one function.

Hope that helps.

Answer 7

!, or factorial is a function. The important and useful characteristic of the factorial function is that at every point x, x! is equal to (x-1)! *X.
it is a special case of the Gamma Function that contains only the integers.

To answer your question, you can't divide two sides of an equation by a function. ! is an abbreviation of an extremely complicated integral.

Answer 8

You can't divide both sides of that equation by ! because ! is not a fixed value- it's just a convenient way of notating "factorial".

Therefore 1=0 is not correct.

It's like saying 50% divided by % is equal to 50. % is not a number so it makes no sense.

Answer 9

1! = 1 and my TI-83 plus agrees with me.

Answer 10

isnt this a philosophy class? I took a class my sophomore year of college that made me solve questions like that but it was for philosophy