welcome to premath in this video tutorial we have got this really interesting question why is 0 factorial equal to 1 and now i will show you a plain and simple proof for this and here's the definition of x factorial as you can see over here let me give you a really simple example let's start off with 5 factorial so 5 factorial could be written as 5 times 1 less of this one that is going to be 4 1 x again 1 less means 3 2 1. so this is called the 5 factorial and likewise a 7 factorial is going to be 7 times 6 times 5 times 4 3 2 1. let me go ahead and manipulate this one so 5 factorial could be written as i can write this 5 right here equal to 5 times this part over here could also be written as times 4 factorial isn't it let me give you one more example so 7 factorial once again we know that 7 6 5 4 3 2 and 1 so this 7 factorial could be written as this 7 write it down over here times this thing the whole par this second part this could be written as 6 factorial isn't it so i can write a 6 factorial so just keep in your mind so therefore based on these calculations that we did these observations we can generalize this thing as x factorial equal to x times x minus 1 factorial now i want to isolate this part so let me go ahead and divide both sides by x so this x and x cancels out so we got x minus 1 factorial equals to x factorial divided by x so thus we got x minus 1 factorial equal to x factorial divided by x now let's go ahead and pick x equal to 1 and put it in this equation so that is once we plug it in x equal to 1 that's going to become 1 minus 1 factorial equals to this is going to be 1 factorial divided by 1 here 1 minus 1 is going to give us 0 factorial equal to we know 1 factorial is simply 1 divided by 1 so thus 0 factorial turns out to be simply 1 and that's the end of the proof thanks for watching and please don't forget to subscribe to my channel for more exciting videos bye