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    (Original post by Felix Felicis)
    Haha, yarp xD


    How about this? Prove that a rational number + irrational number = irrational
    Okays Can I just use any two numbers and prove using that?
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    (Original post by MathsNerd1)
    Could anyone give me another question because I'm starting to get back into the mindset for them


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    Prove n! > 2^{n} for n \geq 4, \ n \in \mathbb{Z^{+}}
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    (Original post by Felix Felicis)
    See that's what the proof is trivial is for but tbh, most people on that thread would decimate these problems within femtoseconds and as AS maths is finished now, it's only A2 candidates left so this thread's died down a bit, so we may as well use it for these lighter problems :ahee:
    The only problem is just that the questions in the proof is trivial are out of my reach, and I find these questions a lot easier to answer. I'm actually very glad that you post these questions as I've learned some new techniques.
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    (Original post by Felix Felicis)
    Prove n! > 2^{n} for n \geq 4, \ n \in \mathbb{Z^{+}}
    Well this one looks quite different, I'll see how far I can go with it before getting stuck


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    (Original post by Felix Felicis)
    Apologies for the ambiguity, I meant:

    irrational + irrational = irrational for all irrational numbers <==== true or false?
    Do you just want an answer or a proof as well?

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    False, I'm pretty sure
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    (Original post by tigerz)
    Okays Can I just use any two numbers and prove using that?
    No, you can't use specific examples
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    (Original post by justinawe)
    Do you just want an answer or a proof as well?

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    False, I'm pretty sure
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    Nah, counterexample or some sort of justification will suffice :awesome:
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    (Original post by Felix Felicis)
    No, you can't use specific examples
    So I would use x? or w/e
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    (Original post by tigerz)
    So I would use x? or w/e
    Yeah :awesome:
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    (Original post by Felix Felicis)
    Yeah :awesome:
    LOOL okays time to neglect chem as usual ;O
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    (Original post by Felix Felicis)
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    Nah, counterexample or some sort of justification will suffice :awesome:
    Can I just be incredibly lazy and say,

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    \sqrt{2} is irrational (not going to bother proving this).

    4957249574 - \sqrt{2} is irrational (DJMayes proved that rational+irrational=irrational earlier).


    \sqrt{2} + {4957249574 - \sqrt{2} = 4957249574 + (\sqrt{2} - \sqrt{2}}) = 4957249574 +0

     = 4957249574

    Which is rational, so the statement is proven false by counter-example.
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    (Original post by Felix Felicis)
    Prove n! &gt; 2^{n} for n \geq 4, \ n \in \mathbb{Z^{+}}
    As imagined the inductive step has just baffled me, I don't know how to show the RHS being less than the LHS in a case of K+1


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    ignore ignore ignore
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    (Original post by justinawe)
    Can I just be incredibly lazy and say,

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    \sqrt{2} is irrational (not going to bother proving this).

    4957249574 - \sqrt{2} is irrational (DJMayes proved that rational+irrational=irrational earlier).


    \sqrt{2} + {4957249574 - \sqrt{2} = 4957249574 + (\sqrt{2} - \sqrt{2}} = 4957249574 +0

     = 4957249574

    Which is rational, so the statement is proven false by counter-example.
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    I was even lazier and said (1 - \pi) is irrational and (1 - \pi) + \pi = 1 which is rational xD
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    (Original post by MathsNerd1)
    As imagined the inductive step has just baffled me, I don't know how to show the RHS being less than the LHS in a case of K+1
    There is absolutely no need for induction.
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    (Original post by Felix Felicis)
    Apologies for the ambiguity, I meant:

    irrational + irrational = irrational for all irrational numbers <==== true or false?
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    Let X be an irrational number then X+(-X)=0 so it's false.

    (2-sqrt3) is irrational and (2+sqrt3) is irrational too so (2-sqrt3)+(2+sqrt3)=4 which is rational.
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    (Original post by Felix Felicis)
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    I was even lazier and said (1 - \pi) is irrational and (1 - \pi) + \pi = 1 which is rational xD
    Same difference :dontknow:
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    (Original post by Felix Felicis)
    Indeed :ahee: Although not that interesting if you cracked it in 2 mins :lol: Just trying to think of random ones off the top of my head :dontknow:

    Irrational + Irrational = Irrational <== True or false?
    False.

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    Take  \pm \sqrt{2} for an easy counterexample.

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    (Original post by Lord of the Flies)
    There is absolutely no need for induction.
    What do you mean?


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    (Original post by justinawe)
    Same difference :dontknow:
    Well yeah but how much effort do you need to put in to write a random number and then copy and paste it xD
 
 
 
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