[Guest]

Math is a beautiful thing because it all fits together perfectly. Because math is so awesome, I had to list another problem, significantly simpler that my last, but just as interesting.

Proof that 1 < 0

0 < x < 1

ln(x) < 0

divide both sides by ln(x)

[ ln(x) / ln(x) ] < [ 0 / ln(x) ]

1 < 0

This should take no time for you math savvy people!

enjoy

[Guest]

I think when you divide by a negative number you have to switch the inequality around.

[bonanova]

I think when you divide by a negative number you have to switch the inequality around.

For discussion, take the inequality 4 < 5.

Multiplying [or dividing] both sides by a negative number changes their signs.

e.g. multiply [or divide] both sides by -1, and see what happens.

(-4) < (-5) which is clearly wrong.

What is preserved about an inequality under sign change is distance from the origin. [absolute value - ignoring the sign]

(-5) is more distant from the origin than (-4) is, just as 5 is more distant from the origin than 4 is.

But (<) deals with being to the left or to the right on the line of reals, regardless of which side of the origin you are.

A sign change makes a mirror image at the origin, which changes that order.

[Guest]

since ln(x)<0, ln(x) is a negative number, so when you divide by ln(x) you have to flip the inequality sign around and you end up with

1>0