Simple. Problem. I think.

Paradoxical Numbers

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Simple. Problem. I think.

#1  Postby Gareth » Feb 11, 2016 5:32 pm

a). If x squared + 1 = 0
b). then x squared is minus 1
c). and x to the fourth power is plus 1,
d). so, x to the fourth is either:
e). 1 times 1, times 1, times 1 ( = +1)
f). or minus 1 times minus 1, times minus 1, times minus 1 (= +1)
g). i.e. the fourth root of x to the fourth must be +1.
h). So, since x = +1
i). then x squared must also be plus 1,
j). but from b) we know that x squared is (also) minus 1.
k). Thus 2 times x squared can be -2, +2 or zero.

From there it would be possible to 'prove' that any integer equals any other integer and thus arrive at any desired result for any calculation.

l). We also notice that substituting either +1 or -1 for x squared in equation a) gives us a result of +2 on the right, so both answers are clearly wrong.

Since the mathematics of quantum electrodynamics -- and quantum theory in general -- rely heavily on such imaginary numbers, one would expect from the above (assuming there is no error or omission in the maths or reasoning above) that:

1), practitioners could routinely obtain predicted results,

2), they would frequently obtain a second, contradictory result (e.g. both plus and minus, 'up' and 'down', wave and particle or 'live/dead cat') and,

3), both their conclusions (from l).) would also quite possibly be wrong, in which case imaginary numbers may not be the most useful tool for understanding quantum phenomena.

Q: Is there any error, omission or unjustified assumption in the workings above?
(There may well be: I'm told I'm a bit of a dunce in maths, and only an idiot would trust my calculations without checking them first. I certainly wouldn't.)

Q: If so, what is it?
Thank you.
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Re: Simple. Problem. I think.

#2  Postby DavidMcC » Feb 11, 2016 5:36 pm

Step g is a non-sequitur.
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Re: Simple. Problem. I think.

#3  Postby campermon » Feb 11, 2016 5:37 pm

There's nothing to see here; Complex numbers.

Move along people.

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Re: Simple. Problem. I think.

#4  Postby Thommo » Feb 11, 2016 5:38 pm

(e) and (f) don't follow from (d).

(g) doesn't follow from (e) and (f).

Since you mention imaginary numbers later in your post I don't really understand why you think they do. i is not equal to either +1 or -1. In general there are are 4 roots of a quartic equation, in this case the fourth roots of 1 are i, -i, 1 and -1.
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Re: Simple. Problem. I think.

#5  Postby scott1328 » Feb 11, 2016 5:42 pm

X^2 + 1 = 0

is false when X is a real number. Ex falso quodlibet.
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Re: Simple. Problem. I think.

#6  Postby DavidMcC » Feb 11, 2016 5:43 pm

Thommo wrote:(e) and (f) don't follow from (d).

(g) doesn't follow from (e) and (f).

...

Stop cribbing my answers! :naughty: :smile:
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Re: Simple. Problem. I think.

#7  Postby laklak » Feb 11, 2016 5:45 pm

i see what you did there
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Re: Simple. Problem. I think.

#8  Postby DavidMcC » Feb 11, 2016 5:49 pm

laklak wrote:i see what you did there

Oh, no! Yet more cribbing! :lol: ... :smile:
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Re: Simple. Problem. I think.

#9  Postby Thommo » Feb 11, 2016 5:50 pm

DavidMcC wrote:
Thommo wrote:(e) and (f) don't follow from (d).

(g) doesn't follow from (e) and (f).

...

Stop cribbing my answers! :naughty: :smile:


To be honest I've stopped reading your posts, so I didn't even notice you'd said a small fraction of the things that I wrote there till I read this one by accident.

Still, nice to see you get something even faintly right for a change. Well done you. :thumbup:
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Re: Simple. Problem. I think.

#10  Postby scott1328 » Feb 11, 2016 6:00 pm

Ooh I have one
Let a=b
Multiply both sides by a: a2 = ab
Subtract b2 from both sides: a2-b2 = ab - b2
Factor the left side: (a-b)(a+b) = ab - b2
Factor the right side: (a-b)(a+b) = b(a-b)
Divide out the common factor (a-b): (a+b) = b
Since a=b, substitute for b: a+a = a
Simplify: 2a = a
Divide out common factor a: 2=1

Therefore all of mathematics is a sham and God exists.
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Re: Simple. Problem. I think.

#11  Postby laklak » Feb 11, 2016 6:03 pm

Divide out the common factor (a-b): (a+b) = b UNDEFINED OPERATION EXCEPTION
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Re: Simple. Problem. I think.

#12  Postby Thommo » Feb 11, 2016 6:03 pm

laklak wrote:Divide out the common factor (a-b): (a+b) = b UNDEFINED OPERATION EXCEPTION


Pay no attention to that man behind that curtain FFS.
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Re: Simple. Problem. I think.

#13  Postby campermon » Feb 11, 2016 6:06 pm

scott1328 wrote:Ooh I have one
Let a=b
Multiply both sides by a: a2 = ab
Subtract b2 from both sides: a2-b2 = ab - b2
Factor the left side: (a-b)(a+b) = ab - b2
Factor the right side: (a-b)(a+b) = b(a-b)
Divide out the common factor (a-b): (a+b) = b
Since a=b, substitute for b: a+a = a
Simplify: 2a = a
Divide out common factor a: 2=1

Therefore all of mathematics is a sham and God exists.


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Re: Simple. Problem. I think.

#14  Postby Gareth » Feb 11, 2016 7:55 pm

DavidMcC.

Thanks for that. I don't get it though. If x to the fourth is 1, what else could x be but 1?
I didn't crib it by the way. I thought of squaring both sides all be myself, so as not to get stuck with impossible square roots.

Laklak: "i see what you did there"
That made me laugh.

scott1328:
"X^2 + 1 = 0
is false when X is a real number."

I agree (obviously). That's why I feel that any maths done using paradoxical numbers must be very questionable.
I liked your version too, even if it does apparently contain a 'UNDEFINED OPERATION EXCEPTION' (?)

The Caerphilly Hypothesis, of course, has no such shortcomings : " Everything is cheese," and its corollary -- "Cheese is everything."

Just waiting for DMcC's answer, then I can have a little nap.
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Re: Simple. Problem. I think.

#15  Postby scott1328 » Feb 11, 2016 8:02 pm

Gareth wrote:DavidMcC.

Thanks for that. I don't get it though. If x to the fourth is 1, what else could x be but 1?
I didn't crib it by the way. I thought of squaring both sides all be myself, so as not to get stuck with impossible square roots.

Laklak: "i see what you did there"
That made me laugh.

scott1328:
"X^2 + 1 = 0
is false when X is a real number."

I agree (obviously). That's why I feel that any maths done using paradoxical numbers must be very questionable.
I liked your version too, even if it does apparently contain a 'UNDEFINED OPERATION EXCEPTION' (?)

The Caerphilly Hypothesis, of course, has no such shortcomings : " Everything is cheese," and its corollary -- "Cheese is everything."

Just waiting for DMcC's answer, then I can have a little nap.
Just waiting for

There is no paradox. You simply lack even basic understanding of highschool algebra.
You had better stick with fucking up aerodynamics and special relativity. At least that way, you are only displaying incompetance at college level subjects.
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Re: Simple. Problem. I think.

#16  Postby Thommo » Feb 11, 2016 8:08 pm

scott1328 wrote:There is no paradox. You simply lack even basic understanding of highschool algebra.
You had better stick with fucking up aerodynamics and special relativity. At least that way, you are only displaying incompetance at college level subjects.


Indeed, next up: Proving √2 is irrational and destroying real analysis, followed by despair and drowning at sea.
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Re: Simple. Problem. I think.

#17  Postby campermon » Feb 11, 2016 8:12 pm

Bar's open people.

I'm buying.

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Re: Simple. Problem. I think.

#18  Postby Gareth » Feb 11, 2016 8:12 pm

That's okay. Look, you guys don't have to keep pointing out that I'm not as smart as I think I am... I have a wife to do that... but thanks anyway.
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Re: Simple. Problem. I think.

#19  Postby scott1328 » Feb 11, 2016 8:13 pm

Thommo wrote:
scott1328 wrote:There is no paradox. You simply lack even basic understanding of highschool algebra.
You had better stick with fucking up aerodynamics and special relativity. At least that way, you are only displaying incompetance at college level subjects.


Indeed, next up: Proving √2 is irrational and destroying real analysis, followed by despair and drowning at sea.

The Pythagoreans killed the man who first demonstrated that √2 is irrational. It overthrew their mathematics until Eudoxus theory of proportion salvaged the mess.
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Re: Simple. Problem. I think.

#20  Postby scott1328 » Feb 11, 2016 8:14 pm

Gareth wrote:That's okay. Look, you guys don't have to keep pointing out that I'm not as smart as I think I am... I have a wife to do that... but thanks anyway.

Listen to your wife. Presumably she loves you.
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