Lab 2 problem # 206

by **jihat777** Tue Jan 15, 2008 1:34 pm

In the instructors explanation, why are negative numbers not tested for case (1)?

Is that based on some condition that he is specifically testing for?

Thanks

by **RonPurewal** Wed Jan 16, 2008 6:04 am

hi :

i'm glad you didn't post the question, because it's an OG question (we are barred from posting those on the site).

negative numbers aren't tested on case one because no negative numbers satisfy the criteria. try it yourself: (negative number)^2 is positive, while (negative number) is of course negative, so there's no way (negative number)^2 can be smaller.

the same logic also explains why there aren't any integers, in case that question was coming next.

by **jihat777** Wed Jan 16, 2008 1:28 pm

For case 1 - you could use a positive fraction and a negative fraction say... -1/2 or 1/2 so both of those in your list would satisfy (1), but would not answer the question definitily as either Yes or No. So wouldn't it be insufficient?

Or is using fractions going outside the criteria.

Sorry for belaboring the quesiton... just wanted clarification.

by **StaceyKoprince** Mon Jan 21, 2008 4:21 pm

I assume you mean statement 1 when you say "for case 1"?

Statement 1 says that x^2 is less than x. You're only allowed to try numbers that make this statement true. A negative number would make this statement false - when you square a negative number, it becomes positive. A positive number will always be greater than the negative number you started with. So it won't be true that x^2 is less than x.

Your instincts are good - you should try positive and negative fractions if you're allowed to. But, in this case, we're not allowed to try negative fractions because they do not make the statements true.