Difference between revisions of "Proof that 2=1"
Shurong.ge (talk | contribs) (→Proof) |
Flashdragon (talk | contribs) (→Note:) |
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4) <math>(a+b)(a-b) = b(a-b)</math>. Factor both sides. | 4) <math>(a+b)(a-b) = b(a-b)</math>. Factor both sides. | ||
| − | 5) <math>(a+b) = b</math>. | + | 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>. | 6) <math>a+a = a</math>. Substitute <math>a</math> for <math>b</math>. | ||
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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.
