Here are 100 free points and you will have to win to get the brainiest

potatoes pt.2

Explanation:

I'll prove that 1 + 1 = 2

Explanation:

The proof starts from the Peano Postulates, which define the natural numbers N. N is the smallest set satisfying these postulates:

P1.  1 is in N.

P2.  If x is in N, then its "successor" x' is in N.

P3.  There is no x such that x' = 1.

P4.  If x isn't 1, then there is a y in N such that y' = x.

P5.  If S is a subset of N, 1 is in S, and the implication

(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:

Def: Let a and b be in N. If b = 1, then define a + b = a'

(using P1 and P2). If b isn't 1, then let c' = b, with c in N

(using P4), and define a + b = (a + c)'.

Then you have to define 2:

Def:  2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem:  1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.

Then 1 + 1 = 1' = 2  Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which  

replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the  

definition of addition to this:

Def: Let a and b be in N. If b = 0, then define a + b = a.

If b isn't 0, then let c' = b, with c in N, and define

a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the  

Theorem above is a little different:

Proof: Use the second part of the definition of + first:

1 + 1 = (1 + 0)'

Now use the first part of the definition of + on the sum in  parentheses:  1 + 1 = (1)' = 1' = 2  Q.E.D.

=)

:)

organisms that are both used in toothpaste as well as cause malaria are protista and monera.

"1. it should be, it has been for about 20 years, and it's really not much different in the end than breeding animals to have particular traits. there are always concerns about genetically engineered animals/plants affecting the environment in unexpected negative ways, but i can't think of an example where the fears didn't turn out to be baseless.  

first, as you point out, it would be a great advance in pharmacology, to be able to tailor drugs and their doses to me. the pros involve better medical treatment. the cons involve privacy issues like insurance companies denying coverage to people with genetic risk factors. looking at dna markers wouldn't affect the frequency of genetic diseases, but it would allow detection of them earlier. and ok, actually i suppose that if people used this information to avoid having children with genetic diseases, some might decrease in frequency."