Hey I'm in Contemp Math, so I'm just studyign but can someone give me examples

To find a counter example to show that each conjecture is false

_______

1./ x^2=x

2. any number divided by itself equal to 1

3. for all x |x-14|<x

thank you!!

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- Sep 7th 2008, 06:07 PMDillon658algebra identity
Hey I'm in Contemp Math, so I'm just studyign but can someone give me examples

To find a counter example to show that each conjecture is false

_______

1./ x^2=x

2. any number divided by itself equal to 1

3. for all x |x-14|<x

thank you!! - Sep 7th 2008, 06:17 PMJhevon
come on, pick a random number. there are only two real numbers for which this works, your chances of being right through randomly guessing are actually pretty good

Quote:

2. any number divided by itself equal to 1

Quote:

3. for all x |x-14|<x

thank you!!

- Sep 7th 2008, 06:19 PMo_O
I think the OP meant to have a square root sign over x^2: $\displaystyle \sqrt{x^2} = x$.

Note that: $\displaystyle \sqrt{x^2} = |x|$ Can you think of a number that will be a counterexample to $\displaystyle \sqrt{x^2} = x$ - Sep 7th 2008, 06:29 PMDillon658
- Sep 7th 2008, 06:38 PM11rdc11
$\displaystyle 0^2 = 0$

$\displaystyle 1^2 = 1$ - Sep 7th 2008, 06:41 PMDillon658
" In a soccer league with 10 teams, each team plays each of the other teams 3 times. How many league games will be played?"

Determine the nth-term formula for a sequence that has the first 3 terms of

9, 12, 15.....

if you can help me with those too? and that last one it messed up

for all x, |x-14|< 14 - Sep 7th 2008, 06:55 PMJhevon
you realize counter-example means here to find a number for which it does NOT work, right? clearly it works for 1...

if you let x = 1, is x^2 = x?

if you let x = 2, is x^2 = x?

by the way, o_O suggested your question might be something else, was he right?

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and for number 2 I got 0?

- Sep 7th 2008, 06:57 PMDillon658
yes 0_0 was correct its all under the square root thingy

and thank you for helping me

quick question

"All ancient greek mathaticians were also philosphers. Euclid was an ancient Greek mathematician, so Euclid was also a philosopher."

Is that inductive reasoning or deductive? - Sep 7th 2008, 07:03 PMJhevon
ok, call the teams team1, team2, etc

and lets think through this.

team1 plays the other 9 teams 3 times each, so team 1 plays 3x9 = 27 games

team2 has to play the other 9 teams 3 times as well. but it already played team1 3 times, so it remains to play the other 8 teams 3 times. thus we have an additional 3x8 = 24 games

team3 has to play the other 9 teams 3 times as well. but it already played team1 3 times AND team2 3 times, so it remains to play the other 7 teams 3 times. thus we have an additional 3x7 = 21 games

.

.

.

.

continue the same reasoning. how much do you end up with?

Quote:

Determine the nth-term formula for a sequence that has the first 3 terms of

9, 12, 15.....

Quote:

if you can help me with those too? and that last one it messed up

for all x, |x-14|< 14

- Sep 7th 2008, 07:06 PMJhevon
ok, then my advice with that question is the same as with the |x - 14| < x question.

did you find an answer yet?

Quote:

quick question

"All ancient greek mathaticians were also philosphers. Euclid was an ancient Greek mathematician, so Euclid was also a philosopher."

Is that inductive reasoning or deductive?

also, you should really ask new questions in new threads. if all your questions are related, then post all at once. we would appreciate it if you are honest and tell us if it is for homework or a take home test or something to be graded. - Sep 7th 2008, 07:12 PMDillon658
ok for one I got 72 games??

number 2 I got 18 just add +3? the determine the formula what gets me

number 3 I got 15? if 15-14 is 1? it cant be greater than 14 - Sep 8th 2008, 01:00 AMChop Suey
For number 2, think of it as an arithmetic sequence with a common difference d. Then, use this equation:

$\displaystyle t_n = t_1 + (n-1)(d)$

...to find the nth formula. $\displaystyle t_n$ is the nth term and $\displaystyle t_1$ is the first term.

$\displaystyle \underbrace{9}_{\text{first term}}, \underbrace{12}_{\text{second term}}, \underbrace{15}_{\text{third term}}, \ldots$

As for number 3:

$\displaystyle |x-14|<x\ \text{for all}\ x$ is a statement that could be either true or false. You need to find a counterexample, which is an example that makes the statement false.

Understand what you are given here. Anything that comes out of an absolute value will be positive. So when is it ridiculous that a positive number is less than a given number?