Unfortunately I have read few proofs and have written fewer. So I am asking for advice on how to write this one so hopefully I can get better at it.(adsbygoogle = window.adsbygoogle || []).push({});

I am to show that

Eq1: Abs[ D[y,x] ] + Abs[ y ] + 1 = 0

has no solutions.

So this is what I was thinking.

Let

f(y) = Abs[ y ]

g(y) = Abs[ D[y,x] ]

Thus we can rewrite Eq1 as

Eq2: f(y) + g(y) + 1 = 0

However due to the Abs operator the domain of both f and g

must be greater than or equal to zero therefore there is no y

in the range of f or g that can satisfy Eq2.

I guess first off, is this proof even correct?

Is there anything I should do to improve it?

Is ok for me to imply and assume the fact that 1 plus a

non-negative cannot be less than 1 thus the sum cannot be

zero? I suppose the answer depends on the audience. Here I

assumed the audience was my college student peers with

the material we have covered to date, including previous

classes, therefore the proof of this fact should be pretty easily

available.

I guess I am most concerned with where to draw the "it's trivial

from here" line. I mean, to be honest, this proof in itself seems

a bit trivial which, ironically, is what makes it hard to write. :)

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# Showing a diff. eq. has no solutions

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