.I need to Prove or Disprove: There does not exist a real number x such that for all real numbers y, xy=1.
This is false. I am going to try to prove it using contradiction.
You mean: "this is true", i.e.: the claim is true, since there indeed is NOT such a number x
Suppose not. That is, suppose that there does exist a real number x such that for all real numbers y, xy=1.
You mean "suppose yes: there is such a number..." . I think you got confused with so many negations.
Let x be any real number r. X=1/r.
So you define ... why to choose the same letter, capital and non-capital, twice? This may help to make things even more confusing.
Let y be an real number r. Y=r/1
And now you've defined so far ...is this really what you meant?
X*Y= (1/r)*(r/1) by substitution
= 1 By algebra.
This is wrong: ...and that's pretty much there is to it.
This is a contradiction because there does exist a real number x such that for all real numbers y x*y=1. **end of proof**
There is no proof at all above of anything. Perhaps you could try the following:
Suppose there exists such a real number . Choose now [tex]
, and now choose say and get that x must equal two different numbers: contradiction and we're done.
Can some someone please let me know if this is a correct way to write it on paper? I am pretty confident, however I would like to make sure, is there anything I can add for correctness?