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Proof that one equals zero (Using Algebra)
Given that a and b are integers such that a = b + 1, Prove: 1 = 0
1. a = b + 1 1. Given
2. (a-b)a = (a-b)(b+1) 2. Multiplication Prop. of =
3. a2 - ab = ab + a - b2 - b 3. Distributive Propoerty
4. a2 - ab -a = ab + a -a - b2 - b 4. Subtraction Prop. of =
5. a(a - b - 1) = b(a - b - 1) 5. Distributive Propoerty
6. a = b 6. Division Property of =
7. b + 1 = b 7. Transitive Property of = (Steps 1, 7)
8. Therefore, 1 = 0 8. Subtraction Prop. of =
Why does 0! = 1 ?
Usually n factorial is defined in the following way:
n! = 1*2*3*...*n
But this definition does not give a value for 0 factorial, so a natural question is: what is the value here of 0! ?
A first way to see that 0! = 1 is by working backward. We know that:
1! = 1
2! = 1!*2
2! = 2
3! = 2!*3
3! = 6
4! = 3!*4
4! = 24
We can turn this around:
4! = 24
3! = 4!/4
3! = 6
2! = 3!/3
2! = 2
1! = 2!/2
1! = 1
0! = 1!/1
0! = 1
In this way a reasonable value for 0! can be found.
How can we fit 0! = 1 into a definition for n! ? Let's rewrite the usual definition with recurrence:
1! = 1
n! = n*(n-1)! for n > 1
Now it is simple to change the definition to include 0! :
0! = 1
n! = n*(n-1)! for n > 0
From Concrete Mathematics p.162 (R. Graham, D. Knuth, O. Patashnik):
Some textbooks leave the quantity 0^0 undefined, because the
functions x^0 and 0^x have different limiting values when x
decreases to 0. But this is a mistake. We must define x^0=1 for all
x , if the binomial theorem is to be valid when x = 0 , y = 0 ,
and/or x = -y . The theorem is too important to be arbitrarily
restricted! By contrast, the function 0^x is quite unimportant.
Originally posted by itsallintheegg
Ponder that one.
Originally posted by Egyptia
reply to post by wishful1gnorance
Wow Wishful I will have to re-read this again, mathematicas and equations are not always my fortay. However, I agree that we are more than just ourselves. Every living thing is more than itself because if it were otherwise, we would exist as our own private universe. We were created after all, and that in itself implies that we are more than just ourselves in our existence.
I'm just not sure why we always have to complicate the obvious with the mental prowess of man and his 'intelligence' separating the very Creator of it all to include only man's reasoning in exclusion of G-d?
I mean isn't that what your equation is concluding?edit on 21-9-2012 by Egyptia because: (no reason given)
Originally posted by ErroneousDylan
Nice thread. Another allegory I like to use to represent the collective consciousness is this. In my eyes, there is only one natural number, and that is 1. The other numbers are just plural versions of 1. So, we can express ourselves as 1, and together, no matter how many people, we are just a plural version of our individual selves.
I am 1, and you are 1, and together we are two 1s.
Originally posted by wishful1gnorance
reply to post by itsallintheegg
Also stated. Thanks again
While I was raised catholic, religion has no place in what I'm talking about.
Please can a mod remove his posts, he's gone of topic. He has no idea what my delivered message is, and is simply replying to the title of my thread.edit on 21-9-2012 by wishful1gnorance because: (no reason given)
Originally posted by r2d246
I hear what you're saying. Life is a big mathamatical equation in so many ways. Shouldn't that make it extremely obviously to you that there is a God, one omnipotent creator, the master of all math who put this matrix together, and also within it explained to everyone the purpose for us being here as outlined in the bible? It's so obvious. As you full well know then as a math whiz that the probability of us being here without it being specifically created in such a format is an impossibility. There's simply way too many perfectly designed scenarios that are all working in harmony to give us life. Therefor the only one thing you have left to do if you haven't already in this vast nothingness is to find God and get to know him. That's your ultimate mission in life. Everything else pales in comparison. good luck.