# Difference between revisions of "Proof that 2=1"

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− | + | ==Proof== | |

+ | |||

+ | 1) <math>a = b</math>. Given. | ||

+ | |||

+ | 2) <math>a^2 = ab</math>. Multiply both sides by a. | ||

+ | |||

+ | 3) <math>a^2-b^2 = ab-b^2</math>. Subtract <math>b^2</math> from both sides. | ||

+ | |||

+ | 4) <math>(a+b)(a-b) = b(a-b)</math>. Factor both sides. | ||

+ | |||

+ | 5) <math>(a+b) = b</math>. Divide both sides by <math>(a-b)</math> | ||

+ | |||

+ | 6) <math>a+a = a</math>. Substitute <math>a</math> for <math>b</math>. | ||

+ | |||

+ | 7) <math>2a = a</math>. Addition. | ||

+ | |||

+ | 8) <math>2 = 1</math>. Divide both sides by <math>a</math>. | ||

+ | |||

+ | ==Error== | ||

+ | Usually, if a proof proves a statement that is clearly false, the proof has probably divided by zero in some way. | ||

+ | |||

+ | In this case, the quantity of <math>a-b</math> is <math>0</math> as <math>a = b</math>, since one cannot divide by zero, the proof is incorrect from that point on. | ||

+ | |||

+ | <b>Thus, this proof is false.</b> | ||

+ | |||

+ | ==Note:== | ||

+ | If this proof were somehow true all of mathematics would collapse. Simple arithmetic would yield infinite answers. This is why one cannot divide by zero. |

## Latest revision as of 09:55, 14 May 2020

## Proof

1) . Given.

2) . Multiply both sides by a.

3) . Subtract from both sides.

4) . Factor both sides.

5) . Divide both sides by

6) . Substitute for .

7) . Addition.

8) . Divide both sides by .

## Error

Usually, if a proof proves a statement that is clearly false, the proof has probably divided by zero in some way.

In this case, the quantity of is as , since one cannot divide by zero, the proof is incorrect from that point on.

**Thus, this proof is false.**

## Note:

If this proof were somehow true all of mathematics would collapse. Simple arithmetic would yield infinite answers. This is why one cannot divide by zero.