Proof 1 Plus 1 Equals 2

Divide both sides by y proof that 2 equals 1 first prev. The table below gives a proof of 1 1 2 based on the proof system described in formal proofs of arithmetic since 1 and 2 don t occur as basic symbols of that system we need to define them as 0 and 0 so the statement to be proved is 0 0 0. Subtract y 2 from both sides 4 x y x y y x y.

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9 9 repeating 10x.

Proof 1 plus 1 equals 2. A proof using beginning algebra the fallacious proof. Put on your thinking cap for this one. I assume you mean 1 9 repeating the standard proof is that 9 repeating 1. Proof that 1 plus 1 equals 2.

Cancel out common factors 6 y y y. Subtract out x for. And cancelling the from both sides gives 1 2. Given 2 x 2 xy.

In an integer series. Substitute x for y by equation 1 7 2 1. Given 2 x 2 xy. Multiply both sides by x 3 x 2 y 2 xy y 2.

And here is the proof. This can be written as step 8. 1 3 is 3 repeating do the math if you don t believe this 2 3 is 6 repeating 3 3 is 9 repeating. Multiply both sides by x 3 x 2 y 2 xy y 2.

The only reason it equals 2 as it stands is because that is what 2 is defined as. The difficulties in proving that 1 1 2 or one plus one is two stems. See if you can figure out in which step the fallacy lies. Another is 9 repeating x.

1 x y. Proof that 1 2 paradox. Factor 5 x y y. This is defined axiomatically pretty much with the axioms of natural numbers.

Natural numbers are ordered so if you add one to a number you get the next number. Not a proof but 2 is defined as the successor of 1 under peano. Cancel out x y term 6 2y y. Subtract y 2 from both sides 4 x y x y y x y factor both sides 5 x y y.

Then step 3. When you think you ve figured it out.