Conjectures and Counterexamples

[Guest]

Hi! i need some help!!

can anyone give me a mathematical example of Conjectures and counterexamples?

i understand the concept of them..i just can't figure out an example of them!!

the example that our teacher provided with us is :

conjecture: if n^2>n
-example: n=-2
~ (-2)^2>2
~ (2)^2>2
TRUE

counterexample:
-example:n=1
~ (1)^2>1
FALSE there for it IS a counterexample


can anyone help me?? thanks in advance for those who can <3

 

[Denis]

Well...
n/4 > 5

n=24: 24/4 = 6 > 5
n=20: 20/4 = 5 = 5
n=16: 16/4 = 4 < 5

 

[pka]

I like \(\displaystyle \L
\begin{array}{l}
\sqrt {x^2 } = x \\
x = 1\quad \Rightarrow \quad \sqrt {1^2 } = 1 \\
x = 4\quad \Rightarrow \quad \sqrt {4^2 } = 4 \\
x = - 1\quad \Rightarrow \quad \sqrt {\left( { - 1} \right)^2 } = 1 \mbox{ OH NO what happened? \\
\end{array}\)

 

[stapel]

can anyone give me a mathematical example of Conjectures and counterexamples?

A "conjecture" is just a supposition; a "counter-example" is a dis-proof of a conjecture. (The opposite would be a proof, which would mean that the conjecture would then become a theorem.)

Conjecture: All cars are female, because they give me nothing but trouble, but purr like kittens as soon as my hubby gets behind the wheel.
Counter-example: My current car, which has behaved quite nicely. :wink:

Conjecture: All computers are female. (Same reason as above.)
Counter-example: .... Okay, so I'm still working on this one.... :shock:

Conjecture: Astrology is a powerful technique for learning about oneself and ones future by observing one's relationship with all seven of our planets.
Counter-example: There are more than seven planets. :roll:

Conjecture: All integers are even.
Counter-example: Three. :lol:

You were only asked for "an" example. I wouldn't overthink the thing. Just state something you know is false, and then give a counter-example.

Eliz.

 

[Guest]

oh wow!!

you guys are amazing<3

thank you all sooo much xD!! ahahh i couldn't put 2 and 2 together xD

thanks again<3