Algebra Gone Haywire
Mar 21, 2021 18:34:07 #
There is one flaw in this set of equations, leading to an impossible conclusion that 1=2. Can you find it?
Mar 21, 2021 18:38:20 #
Mar 21, 2021 18:48:02 #
ZtaKED
Loc: Lakes Region, New Hampshire & NE Florida
crphoto8 wrote:
In the fourth equation you have a zero, i.e. (a-b) multiplier.
Mar 21, 2021 19:05:29 #
crphoto8 wrote:
In the fourth equation you have a zero, i.e. (a-b) multiplier.
Another way to say this is that the third equation simplifies to 0=0. Everything past that (except the last “equation,” of course) is just different ways of saying the same thing.
Mar 21, 2021 19:33:02 #
Mar 21, 2021 19:38:29 #
Mar 22, 2021 10:00:44 #
Mar 22, 2021 14:58:42 #
RichKenn
Loc: Merritt Island, FL
If 1 is correct, then 2 is correct. 3 and 4 solve to 0=0. All the rest are wrong. I don't see any division anywhere.
Mar 22, 2021 16:40:23 #
gbushaw
Loc: Washington State
The "cancellation" of (a-b) from both sides of the equation that occurs when you go from step 4 to step 5 is really dividing both sides by (a-b), which is dividing both sides by zero, which makes everything that follows nonsense.
Mar 22, 2021 17:14:03 #
Mar 22, 2021 17:25:11 #
gbushaw
Loc: Washington State
You're right. b=b+b can be true only if b=0, but the problem occurs with the division by zero which gets you from line 4 to line 5.
Mar 22, 2021 21:38:27 #
A side note, my algebra teacher showed us that in 1953. Second year of high school.
Mar 22, 2021 23:07:30 #
bobbyjohn wrote:
There is one flaw in this set of equations, leading to an impossible conclusion that 1=2. Can you find it?
If we assign the value
a=1
b=1
then;
Line 1 1=1
Line 2 1=1
Line 3 0=0
Line 4 0=0
Line 5 1=2
Line 6 1=2
Line 7 1=2
Line 8 1=2
From line 3 and onwards we get a different result
From line 5 and onwards would be false
If we assign the value
a=2
b=2
then;
Line 1 2=2
Line 2 4=4
Line 3 0=0
Line 4 0=0
Line 5 2=4
Line 6 2=4
Line 7 2=4
Line 8 1=2
and if we assign the value
a=3
b=3
then;
Line 1 3=3
Line 2 9=9
Line 3 0=0
Line 4 0=0
Line 5 3=6
Line 6 3=6
Line 7 3=6
Line 8 1=2
As shown we can clearly see that some of the equation do not equal or can be a derived from the others hence they can not work together as a series.
Mar 23, 2021 09:20:47 #
I failed algebra 4 times and took it a fifth time in college. The professor took pity on me and gave me a "D". I swore I'd never take another math course. My grandson is breezing through differential equations. I'm not sure if he's my prodigy.
Mar 23, 2021 13:42:35 #
gbushaw
Loc: Washington State
It is clear from all of your examples that there is a problem in going from line 4 to line 5. That is where the (admittedly disguised) division by zero occurs. That IS the problem.
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