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[Iceblaster]

-SHIT WRONG THREAD-

[frostshotgg]

"Inequations are exactly the same as equations."
What is this I don't even.

I think he was saying they can be manipulated like equations.
X^2 < Y^2 can be manipulated to X < Y just the same as X^2 = Y^2.

[Dutchling]

It's X < Y or X < -Y

Just try it with 5 and -6.

[Urist Imiknorris]

It's X < Y or X < -Y

Just try it with 5 and -6.

X < ±Y.

[Helgoland]

It's X < Y or X < -Y

Just try it with 5 and -6.

X < ±Y.

Not for X = Y = 0

[Urist Imiknorris]

But then the original inequality wouldn't be true.

[Helgoland]

But then the original inequality wouldn't be true.

Yeah, it doesn't hold in all cases.

[MagmaMcFry]

"Inequations are exactly the same as equations."
What is this I don't even.

I think he was saying they can be manipulated like equations.
X^2 < Y^2 can be manipulated to X < Y just the same as X^2 = Y^2.

I'd say they're the same in that they specify relations between variables. Obviously equalities are much more powerful in most systems, but they're the same mathematical thing.

[Oliolli]

It's X < Y or X < -Y

Just try it with 5 and -6.

X < ±Y.

X < |Y|

[kaian-a-coel]

It's X < Y or X < -Y

Just try it with 5 and -6.

X < ±Y.

X < |Y|

You win a cookie.

Inequalities are exactly the same as equations, with ONE exception: if you multiply by -1 (or -anything really), you reverse the sign of the inequation. That's pretty much all.

[Darvi]

Also, there's a couple extra steps after finding the zeroes.

[ZetaX]

Inequalities are exactly the same as equations, with ONE exception: if you multiply by -1 (or -anything really), you reverse the sign of the inequation. That's pretty much all.

Sorry, but that's just plain wrong. Apart from several other exceptions you are missing (like division, power, ...), their behaviour is also different. They for example lack reflexivity which is probably the most often used property of equations. Also, inqualities are far less often defined than equalities, e.g. in polynomial rings or complex numbers.

[Helgoland]

Inequalities are exactly the same as equations, with ONE exception: if you multiply by -1 (or -anything really), you reverse the sign of the inequation. That's pretty much all.

Sorry, but that's just plain wrong. Apart from several other exceptions you are missing (like division, power, ...), their behaviour is also different. They for example lack reflexivity which is probably the most often used property of equations. Also, inqualities are far less often defined than equalities, e.g. in polynomial rings or complex numbers.

Yeah, you need an ordered field to have inequalities, but most people only ever use the real numbers - for all practical purposes, inequalities and equalities behave quite similarly. Think of it like this: X < Y <=> (\exists epsilon > 0 so that X = Y - epsilon). If you just run with that, you're golden

[hops]

I find it a little bit sad that people are arguing over things that you're supposed to learn in schools.

[Helgoland]

That's because 'kind of like' is kind of vague~