O.K IWAITED to long and it is getting late .Here is aproof that 1+1=2
1)for all x and for all y(x +Sy =S( x+y)) A peano axiom
2) 1 +S(0) = S( 1+ 0) from 1 and using Univ.Elim. where we put x=1 and y=0
3) for all x (x + 0 =x ) A peano axiom
4) 1 + 0 = 1 from 3...
O.K With such a small proof WHAT ABOUT THE FOLLOWING PROOF??
for all x and for all y(x>=0 and y>=0 -------> ( sqroot(xy)=sqroot(x).sqroot(y) ))
CAN YOU DO IT STEP WISE?
Maybe not you CRGreathouse but in another thread where i was acussed of not knowing the number pi (the Greek invented number) when i responded back the got so ungry that they deleted my posts.
It means that you cannot apply contradiction if the theory is incosistent.
Because in incosistent theories somewhere you will get a contradictory statement hence when you work by contradiction you will not know if you meet this particular statement and hence contadiction has no value.
if the theory is not consistent, then a contradiction doesn't work.
I ask you again: Do you know how contradiction works?
I will show you for the last time how contradiction works.
In a proof by contradiction you ALWAYS END UP with 2 contradictory statements i.e.
R \wedge \neg R
Then study...
The point with you guys is that you write nonsense all the time and if somebody asks you a question with respect to your nonsense and illogical mumbling you get angry.
What actually happens is the following:
you read a couple of things in a couple of books and then you come here and you throw...
THE FUNCTION f(x)=2x+1 where f:N------->R HAS NO LIMIT AT X=2 BECAUSE X IS NOT A POINT OF ACCUMULATION ,BUT IT IS CONTINUOUS AT X=2.
THE SECOND FUNCTION IS NOT MINE IT IS A PROFESSOR"S FUNCTION AND HE SAYS THAT THE FUNCTION CAN HAVE ALIMIT AT X=0 which is 1,and he proves that.
I SUGGEST you...
The following will show you why Now we must be very careful to distinguish between an implication and a logical implication. We say P implies Q noted as P---->Q and this can be true or false depending on the values of p and q. And if p is false and q true then P--->Q is true A thing that...
Deacon John, can you tell me please using your definition of limit what IS the following limit.
1) lim 2x+1 as x-------> 2 where f:N------>R where N is the natural Nos and f(x)=2x+1
Does the following function has any limits within its domain and if yes how many?
f={(1/n,1+2^-n):nεΝ}