Difference between revisions of "Proof that 2=1"
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+ | ==Proof== | ||
+ | |||
1) <math>a = b</math>. Given. | 1) <math>a = b</math>. Given. | ||
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8) <math>2 = 1</math>. Divide both sides by <math>a</math>. | 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. |
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.