Mathematics

copper.hat

9:08 PM

Durrett is very dense, not really introductory.

Balarka Sen

Agreed, although I used it as such.

copper.hat

@pritchard why don't you write out a truth table and investigate.

pritchard

I've never heard of truth table

lone student

@robjohn My reputation is not enough, unfortunately. You're probably talking about "deletion votes".

robjohn

@lonestudent It is being closed, probably because I posted an answer and brought attention to it. When it is closed like this, it is usually on the deletion path.

copper.hat

9:14 PM

@pritchard it is unusual to deal with logic and not have had exposure to truth tables.

robjohn

Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results...

@pritchard that has some introduction

copper.hat

@pritchard what do you mean when you write $C\Leftrightarrow D$?

lone student

@robjohn Yes I saw it now (upvoted) , there are 3 closing votes. The address where all the closing votes came from is known. All coming from "one room". Now you know too.

pritchard

9:34 PM

That C is true if and only if D is

It is not actually a logic question but I am trying to solve a math problem and use this fact

I can't really understand the wiki article but I think my statement was true. Would it be because $B,C\Leftrightarrow D$ is equivalent to $C,B\Leftrightarrow D$?

Ted Shifrin

As you stated it originally, it is very false.

copper.hat

@pritchard If you are given that $B$ is true, how can that have any bearing on the truth of $C\Leftrightarrow D$?

For example, suppose $B$ is "today is Wednesday" and $C$ is "I am 5' tall" and $D$ is "I am 60" tall".

It is certainly not true that "today is Wednesday" iff "I am 60" tall".

AMDG

9:54 PM

@copper.hat Forgot to account for "Super Meal Wednesdays" where you eat a larger meal than normal causing one to gain a few adipocytes on the soles of one's feet, making you 60.000001 inches tall.

robjohn

@lonestudent I found an older post which asks pretty much the same question. I closed it as a duplicate rather than have it closed as a PSQ, which it is not.

o.9

sounds good

I answered one of Peter John's questions

not gonna do the same mistake

robjohn

what happened?

o.9

firstly it got deleted when I was about to submit my answer

It later got undeleted so I was able to type it up again

and then my question got ignored for 3 hours and someone elses answer got accepted so w/e

copper.hat

@AMDG :-)

lone student

10:00 PM

@robjohn The EoQS announcement is almost too recent. The question answered is very old. How accurate is it to apply EoQS to a rather old question? The reason for the closing that the problem is PSQ, which is based on EoQS, I think.

o.9

@lonestudent join the club

Ted Shifrin

Am I collecting club dues?

robjohn

@lonestudent I think anything 2015 or after is fair game.

o.9

why 2015?

pritchard

@copper.hat Wouldn't it be "today is Wednesday and I am 5' tall iff I am 60" tall"? Which is true since today is always Wednesday?

o.9

10:04 PM

sure

oh it seems he deleted it twice and changed it a bit

and never even commented anything to me

what a legend

lone student

@o.9 Why?

AMDG

@pritchard ~~I thought the horse's name was Friday...~~

o.9

You don't have to join the club if you don't want to

robjohn

@o.9: I see that the context that was in that question has been removed (it was replaced by some discussion we had that I abandoned while I was writing my answer, and then that was removed as well). The question is in danger of being closed and deleted now.

o.9

that moment when you add an unnecessary tag to your question and get goldhammered math.stackexchange.com/questions/4216937/…

robjohn

10:17 PM

@o.9 If it's a duplicate, it's a duplicate; but yeah, I see what you mean.

is it a duplicate?

o.9

I'm not sure

OP edited it to say it isn't

I just posted because I thought it was funny :/

Ted Shifrin

10:38 PM

@pritchard: Let's try a mathematical version. B: $I\subset\Bbb R$ is a closed interval. C: $f$ is continuous on $I$. D: $f$ is uniformly continuous on $I$. Then $B\implies (C\iff D)$. What about $C\implies (B\iff D)$?

Or C: $n$ is an even integer. D: $n+1$ is an odd integer. B: $2n$ is an even integer.

pritchard

I see the second one: B implies C iff D, but not C implies B iff D. I cannot solve the first one.

So my original proposition was incorrect

Ted Shifrin

The first one fails likewise.

Transcript for

$Mathematics$ Mathematics