counter example

[jonabiday]

pls help me fine counterexamples to make this false

1. x, x>1/x


2. x, x+x >x

 

[skeeter]

think about trying a negative value for x in both inequalities

 

[Harry_the_cat]

1. think when they might be equal
2. think when they might be equal, or think negative

 

[jonabiday]

think about trying a negative value for x in both inequalities

thank u

 

[pka]

pls help me fine counterexamples to make this false
1. x, x>1/x

Please tell me what this notation means.
\(\large x,~x>\dfrac{1}{x}\) ?? For example what does the comma do, \(x,\)??

 

[skeeter]

Please tell me what this notation means.
\(\large x,~x>\dfrac{1}{x}\) ?? For example what does the comma do, \(x,\)??

I interpreted it as

[MATH]\left\{x \, | \, x > \dfrac{1}{x} \right\}[/MATH]

 

[pka]

I interpreted it as
[MATH]\left\{x \, | \, x > \dfrac{1}{x} \right\}[/MATH]

well ok, but are you sure? Have you really seen that in some mathematics textbook or even a logic text?
Are you implying that we should guess at what a post means?
If you are then I totally reject that idea.

 

[Steven G]

Come on, the problem is asking to find an x such that x > 1/x is false

 

[pka]

Come on, the problem is asking to find an x such that x > 1/x is false

Come on yourself, what in that notation means that?
Show us a textbook, any textbook, that uses that notation.
There may well be individual lectures who use it. But so what?
I still insist that all non-standard notation must be defined.

 

[Dr.Peterson]

pls help me find counterexamples to make this false

1. x, x>1/x
2. x, x+x >x

This seems to be saying that each line is a statement that is to be proved false by counterexample. The only way I can read them as statements is to suppose it is "[MATH]\forall x, x>\frac{1}{x}[/MATH]". Possibly the special symbol was dropped.

I interpreted it as

[MATH]\left\{x \, | \, x > \dfrac{1}{x} \right\}[/MATH]

the problem is asking to find an x such that x > 1/x is false

It isn't described as a set to be determined, or a value to be found. But Jomo's version is more or less equivalent to my version, so one way or the other it is all that makes sense.

 

[skeeter]

well ok, but are you sure? Have you really seen that in some mathematics textbook or even a logic text?
Are you implying that we should guess at what a post means?
If you are then I totally reject that idea.

There’s no “we” here, just me. If I’m wrong, mea culpa.