does every proof have to have a given?
113690
No.  Deductive proofs start from a "given", that is, a fact accepted as true or a theorem previously proven to be true.  But other kinds of proofs start with an assumption that the theorem to be proved is not true, and from that assumption derive some contradiction, thus proving that the theorem itself is true.\n\nAn example would be the proof that there is no highest prime number, which goes like this. Assume that there is a highest prime number.  Call it x.  Now consider the number x! + 1.  (X! is X times X-1 times X-2 all the way down to 1.)  Since x! is divisible by 2, x! + 1, being just 1 more than x!, is not divisible by 2.  Similarly, x! + 1 is not divisible by 3, 4, or any other integer up to and including x.  Since x! + 1 is not divisible by any number up to x, either it is prime, or it's prime factors are larger than x.  But that contradicts our assumption that x is the largest prime.  Thus, our assumption is false.  QED.
852147
it is not true\nbut i have no proof
626246
ok prove it first --- I have a very HIGH bar set for proof.
1018829
None that has been proven.
563765
Definitely B. Any hypothesis by definition must be able to be tested and disproved.
1078520
Boo made two glaring errors in your answer.\n\nThe first is that the law does not require "beyond a shadow of a doubt" in either criminal or civil cases.  In criminal cases the requirement is "beyond reasonable doubt" and in civil it is "proponderence of proof"\n\nThe second is when you say "whether or not you can prove beyond a shadow of doubt that you aren't guilty of what you are being accused of."  This is absolutely false.  The defendent is never required to prove that they aren't guilty--the prosecution ALWAYS has the onus to prove that you are.
208197
If the PROOF is there then most definitely.
908666
Believing is one thing.  Knowing is another.  As most people have said in here, yes you can believe in whatever you want.  That doesn't make it the truth.  And NO, not everyone has to believe in something.  What everyone should have is the knowledge of the truth and the openmindedness to receive the truth.  Not mumbo jumbo from books that you just accept as your truth.
918061
Yes,\nbecause you cannot have two things contradicting each other yet both of them are correct. for example, a>= b and a<b , they cannot be both correct.\n\nWhich one is correct then? well that's for you to find out.\n\nRegards
967058
It depends on what you are wanting to prove. Generally speaking, when you substitute numbers, you are restricting to a specific example. You cannot prove a general result by only looking at specific examples (unless you somehow show those specific cases give *all* the possibilities). However, you *can* show a result is false, if it is false for some specific example, so to show a general result is false, it is enough to 'plug in numbers'.
271648
boy we carry those text books along with us\nif u want us to prove then provide the theorem plz
700964
Verify, validate, substantiate, prove it,
733260
I doubt it.\nHow could someone prove it to be?
153034
No, nobody really can prove it, with assuming several axioms\nfirst. There are certain things you have to assume are true in your universe, without necessary being able to check them. From those axioms, you can derive conclusions (theorems) that are always true, but only in that particular\nuniverse. The discussed operation of addition is one such theorem. If you assume that the axioms of natural numbers are true, then this addition becomes quite trivival. If you assume those axioms of natural numbers to be false, then the above operation of addition might become false with a different set of supposition. In other words, only with the facts given, one cannot prove, nor disprove, the fact of addition. It all depends on the set of assumptions you would have made before adding the two ones.
658128
There is no way to prove a negative.  You are asking me to prove that something doesn't exist.
56339
I am not exactly sure what you mean by "P" at the end of the statements, but there are commonly accepted symbols for "for all" and "there exists." You need visualize this to understand it, so click the link below in "sources" to see the answer graphic hosted at my website www.calculus-help.com. Right now, Yahoo! answers, as far as I can tell, doesn't allow graphics, which makes it tricky to answer ANY math questions.
1082940
The faithful don't believe without proof. They do not run out and buy every product they see advertised. They read Consumer Reports just like the rest of us. If I tried to sell a theist a "magic potion" that would turn him invisible, or told him that his wife was cheating on him, he would ask for proof.\n\nWe only extend our need for proof one step further. We don't see why proof is needed in every aspect of existence except one.