Is W greater than 1?

[angelapeltzer]

Is W greater than 1?
(1) W + 2 > 0
(2) w^2 > 1

Answer is E.

I guessed C as w > -2 and w is either W<-1 or W>1. If W must be greater than -2, it can't be less than -1 but would need to be greater than 1.

I'm not sure why it is E.

Thanks for your help!

- Angie

[RonPurewal]

If W must be greater than -2, it can't be less than -1

Sure it can. There are lots and lots and lots of w's between -2 and -1.
say, -1.5, or -1.99999, or -√3, or whatever.

The problem here is that you're assuming, for no reason, that w is an integer.
Oops.

Now you know what to double-check next time.

[MohamadT743]

Isn't square root of statement 2 => W > 1 ?


sqrt(W^2) = W? or +W and -W?

[tim]

sqrt(W^2) = |W|

[RonPurewal]

Isn't square root of statement 2 => W > 1 ?


sqrt(W^2) = W? or +W and -W?

When these sorts of issues arise, the best way to build intuition is to investigate.
I.e., plug in specific numbers, and watch what they do.

In the case of "w^2 > 1", it should only take you a few plug-ins to realize that:
• w = positive and w = negative have the same result;
• positive numbers ≤ 1 (and, likewise, negative numbers ≥ -1) don't work;
• positive numbers > 1 (and, accordingly, negative numbers < -1) DO work.

[RonPurewal]

Tim's statement above (that w^2 can be reduced to |w|) is true, and can be useful if you already have the corresponding intuition.

On the other hand, if you haven't developed that intuition, then statements like "√(w^2) = |w|" are more or less completely useless.
If it's just a bunch of random symbols, you're not going to be able to figure out what to do with it.

[tim]

If it's just a bunch of random symbols, you're not going to be able to figure out what to do with it.

This is probably true for every math formula ever. As Ron indicates, no amount of memorization of formulas will help if you don't know what to do with them.

[sahilk47]

Isn't square root of statement 2 => W > 1 ?


sqrt(W^2) = W? or +W and -W?

When these sorts of issues arise, the best way to build intuition is to investigate.
I.e., plug in specific numbers, and watch what they do.

In the case of "w^2 > 1", it should only take you a few plug-ins to realize that:
• w = positive and w = negative have the same result;
• positive numbers ≤ 1 (and, likewise, negative numbers ≥ -1) don't work;
• positive numbers > 1 (and, accordingly, negative numbers < -1) DO work.

Hi Ron

I have had this doubt on Modulus function for some time and I have found myself misinterpreting the Modulus function a few times. As you discussed in the above mentioned post : positive numbers > 1 (and, accordingly, negative numbers < -1) DO work
Does Mod w > 1 imply w > 1 and w < -1, or, Mod w > 1 imply w >1 or w < -1 ?
This is a very basic doubt but I feel I am not completely clear about this interpretation.

Thank you!

[RonPurewal]

'w < -1 AND w > 1' is clearly impossible, so that leaves just one possibility.

[sahilk47]

'w < -1 AND w > 1' is clearly impossible, so that leaves just one possibility.

Got it! Thanks!

[RonPurewal]

sure.

the nice thing is that, in MOST cases in which you might be debating whether to use 'and' or 'or', there will be one very obvious meaning... and, if that's the case, your word choice is a non-issue.

this case is a nice example: if you write 'w < -1 and w > 1' then that's technically an impossible statement... but it's absolutely clear what you mean, so there's no reason that this linguistic issue should get in the way of your work.

(as an analogy, many native english speakers will say "i could care less" when their actual meaning is "i couldn't care less"... but in both cases the intended meaning is obvious, so there's no issue.)