Inequalities Algebraic Conventions: Why is it incorrect to write "-2 > x > 2"?

Jim77

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Inequalities Algebraic Conventions: Why is it incorrect to write "-2 > x > 2"?

Hi all

Wonder if someone could point me in the direct of a good resource that explains the algebraic conventions of writing inequalities?

For example can someone explain to me why it is incorrect to write the inequality -2 > x > 2 ? Is it something to do with a non-continuous interval? I presume it should be written as x > 2 or x < -2 ?

Also should x is greater than 2 be written as x > 2 or as 2 < x ?

Any hard and fast rules would be appreciated.

thanks

Jim
 
… can someone explain to me why it is incorrect to write the inequality -2 > x > 2 ?
That says number x is both smaller than -2 and bigger than 2, which is impossible.


Is it something to do with a non-continuous interval? I presume it should be written as x > 2 or x < -2 ?
Yes, that's it. Separated sets need separated inequality statements. Note the difference between OR and AND.


… should x is greater than 2 be written as x > 2 or as 2 < x ?
I would say, if you want to write:

"x greater than 2" use x > 2

"2 less than x" use 2 < x

Inequality statements may be read forwards or backwards. Reading each (above) backwards gives the other; so both inequalities mean the same thing. (On the Real number line, x is to the right of 2.) :cool:
 
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I would say:

"x greater than 2" is x > 2

"2 less than x" is 2 < x

Reading each backwards gives the other; both statements mean the same thing. (On the Real number line, x is to the right of 2.) :cool:

Thanks for your response.

So are you saying that in essence it does not matter which way it is written? Or is there a convention? I know that in algebra there is a convention to write variables in alphabetical order for example a+b+c=d ?
 
… So are you saying that in essence it does not matter which way it is written? …
I'd say the convention is: write it how you would say it out loud.

If you're saying x is greater than 2 (when stating a domain, for instance), then write x > 2.

In different situations, you might want to say that 2 is always a smaller number than x (when explaining a proof, for instance). Then you could write 2<x.

In each situation, write it how you'd say it. :cool:


It might be "unconventional" to see 10 > N > 0 written, but it means the same as 0 < N < 10.
 
I'd say the convention is: write it how you would say it out loud.

If you're saying x is greater than 2 (when stating a domain, for instance), then write x > 2.

In different situations, you might want to say that 2 is always a smaller number than x (when explaining a proof, for instance). Then you could write 2<x.

In each situation, write it how you'd say it. :cool:


It might be "unconventional" to see 10 > N > 0 written, but it means the same as 0 < N < 10.

Thank you for your time and have a great day! :)
 
Also should x is greater than 2 be written as x > 2 or as 2 < x ?

Any hard and fast rules would be appreciated.

thanks

Jim
As long as the arrow (of the less than or greater than symbols) points to the smaller value it is ok, that is it is not wrong. I agree with mmm444bot about writing it as you say it.
 
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