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22:00
Are you thinking that your proof by contradiction is an actual proof? It's a mess, isn't it?
This is not how contradiction works.
@TedShifrin no, I just want to formulate all possible directions first (for myself)
You have not set up contradiction correctly at all.
to see if one is easier than the other
You want to assume both the hypothesis and the contradiction of the conclusion.
can you explain in terms of a->b?
where my mistake is I mean
22:02
So you should suppose that you have an integer $x$ that is not the square of an integer and whose square root is rational.
You must then show this combination is impossible.
@SAJW note that your statement can be reduced to the form $\forall x (A \rightarrow C)$.
@leslietownes My question was somewhat vague.
:)
That’s more or less all the information I have. If you like, $n\in\mathbb{N}$ for sure. Then I guess $n\to\infty$ is a must, since anything else can be computed by plugging it into whatever it is one is taking the limit of.
or more correctly, $\forall x \forall n (x \in \mathbb{Z} \land n \in \mathbb{Z} \land A \rightarrow C)$
what's A and C? (i guess c=NOT complex :P )
antecedent and consequent
22:07
schn that would be the orthodox answer. a limit at some other point would just be the value.
so you should first state your antecedent very clearly. as you can see from the logical equation the status of $n$ and $x$ do not enter into what we're speaking when we say antecedent and consequent
an antecedent and a consequence are only the two sides of the arrow $\rightarrow$
i.e., the two propositions of the implication
I recommend sticking to words over symbols
Me TOOOOOO. This whole thing is too formal, and really little understanding.
22:09
@SAJW If I tell you to prove that $\sqrt2$ is irrational, how are you going to proceed?
It's a sad day when both Thor and Leslie agree with Ted (or vice versa).
@SAJW so the first thing you should focus on is to be really sure what the antecedent is, if you want to do proof by contrapositive
proof by contradiction
it makes me feel old and I really shouldn't
Right, @SAJW. You have no other option. Why?
Now, that is the question!
22:10
Agreeing with Ted makes you feel old, @Thor?
i'm young. i turned 20 yesterday.
Ever the prevaricator.
@shintuku I'm honest, never come to that word.
I say HYPOTHESIS and CONCLUSION.
i'm looking forward to having a fun time in my 20s.
22:12
yeah hypothesis and conclusion works too
@leslie And your daughter will be in her 40s.
@SAJW "If x = 2, then x is positive". The hypothesis is "x = 2", the conclusion is "x is positive" and the entire statement is true
Also I tried to cheat via the question "search", when you enter a question on MES, to no success.
"If x = 2, then x is negative". The hypothesis/antecedent is "x = 2", the conclusion/consequent is "x is negative" the entire statement is false
with both leslie and you, yes
22:13
i forgot about my daughter, i will have to account for her in my new narrative.
maybe she isn't my daughter. people give birth all the time, that doesn't mean they're mine.
So, my hypothesis is "for all $x\in z$ this holds true: if there is no $n\in Z$ such that $x=n^2$ ???
@SAJW: Perhaps the short little appendix I wrote for my algebra book on basic logic and proofs (and I mean short) might help you a little. It's a couple of pages.
the antecedent would be: there is no $n \in \mathbb{Z}$ such that $x = n^2$
you should also read ted's suggestion
"you should also read ted's suggestion" should be the title of this chat.
@TedShifrin available for free? (?) Just asking
22:19
Can you download that in a readable fashion?
this is exactly it, read and understand this
@TedShifrin yes
Maybe a slightly more concrete treatment will help you. If not, it doesn't hurt my feelings :)
I love exercise 6 :P
that's clever, i like that too
The guy that wrote Foxtrot was a mathematician, I think.
22:22
@TedShifrin I'd like to learn it from the Pike, if that is sayable.
I don't know what this means.
are you german?
yes
yeah, I don't think that phrase translates
Was bedeutet das?
22:24
I want to learn it from the very basic level. probably
Deutsch ist die Sprache des Logiks
pike meaning medieval people who fought with pikes? what is the origin of that phrase?
Well, symbols don't necessarily make things basic or understandable. Anyhow, try reading what I wrote. If it helps, it helps. If not, ...
The exercises might be helpful.
If that silly image isn't readable, I can send the pdf in email to anyone who wants.
it's readable here.
It looks tiny to me.
22:26
i can click right into it and read it.
Oh, yeah, with the correct click, it's fine.
it's like "to learn it from the ground up"
@leslietownes that's the first weapon military recruits used to be taught
that makes a lot of sense.
I hope that doesn't mean spending months on the ZF axioms.
pikish weapons are the easiest to learn
22:28
you can learn to shoot with less time than pike. pike seems weird because the opponent is very close and it is easier to shoot them before they do that.
if you ever find yourself in the medieval ages and must defend your village with little knowledge of warfare, pikish weapons are your best bet
i'm not a military theorist, i'm just thinking out loud.
or if you don't have guns
I'm opposed to militarism.
I think that phrase is older than guns
22:30
And with the murders every day with idiots in the US having guns, I'm opposed to guns in general.
or at least older than the systematic use of guns in the military
ted and i agree for the thousandth time.
Damn.
So what are your answers to #6? :D
gimme a sec
I would say agreeing on this matter is not very noteworthy, but I'm afraid it is for you guys
22:31
What's hysterical is that every kid has pulled this maneuver on his parents.
@Thor, by "you guys" you refer to our country of residence, not us individually.
yeah
Yup.
It's OK. Democracy is about to be exploded into smithereens here and Britain both.
i'm building a little wall around my house that i will defend with pikes.
@Leslie: How many times has your daughter pulled this stunt?
@TedShifrin the statements have no truth value
22:33
maybe three hundred.
Thought so.
And the usual conclusion of the kid is ...
he can't know
the usual format is, you can do x if you simply eat more of your vegetables. she puts one more piece of carrot in her mouth and says "i ate more of my vegetables."
the kid can't know
And yet 99.9% of kids will invite Marcus over.
Tacit approval.
22:35
he's a liar, a scam, he can't know
@Leslie: That's a different maneuver. She got you good.
That's why having this appear in a comic strip was so hysterical.
nobody will find any of this funny when she rules the world in about 20 years
I'll be dead.
you might not, ted, and if you're around the universe will need you.
but she'll do something awful, 20 years from now. that's assured.
Dubious on both counts.
@shintuku Of course you are correct, but do you not agree that almost every child on earth will do this and then invite his friend, saying that his parents said he could?
22:39
this wouldn't stand in court, he needs a truth value somewhere
I'm not convinced that lawyers/judges are such good mathematicians.
Look at Leslie, for example.
i guess they would go with: would it be reasonable to assume from this that marcus was allowed over
see, reason has nothing to do with logic
what has the world come to
i actually agree with ted on this.
Oh, I was hoping you wouldn't.
The few math majors I've taught who went to law school seem to have excelled.
the statistics on the LSAT say that math majors do better than anyone else. as a class of subjects.
22:42
better than philosophers?
One of them quit law and decided to teach high school in a not-so-good area of Atlanta ... and raise his kids while his wife lawyers along.
hello everyone
including philosophers, yes.
Hi, vitamin d.
23:05
just to ask: theorem=hypthesis and conclusion
a theorem is a true statement, a true statement can be or contain an implication, an implication has a hypothesis and a conclusion
why is it then called theorem and not a fact?
a theorem is a fact but not all facts are theorems. a theorem is usually a noteworthy fact about mathematics
mathematics books typically build towards theorems, and seek to expose the necessary requirements in order to prove theorems
23:32
@leslietownes is D bounded? does it necessarily have a sup?
I've worked too long on a question and I'm not sure I even want to post an answer. I feel as if I've wasted a lot of time. :-(
Though, I just had an idea that might make it worth posting. Now I have to work that idea through.
23:51
Good question? @robjohn
nvm
(edited: i just needed some definition of the integral, found it)

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