Difference between revisions of "Proof that 2=1"
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==Note:== | ==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. | 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. | ||
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| + | ==Alternate Proof== | ||
| + | Consider the continued fraction <math>3-\frac{2}{3-\frac{2}{3-frac{2}{3- \cdots}}}.</math> | ||
Revision as of 14:40, 27 January 2022
Contents
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.
Alternate Proof
Consider the continued fraction 
