Math Fun

Yeah, and of mathematicians and Nobel prize-winning economists and authors of encyclopedias on philosophy, who apparently also foolishly believe that deducing a proposition X is the same thing as deducing a proposition ~(~X). How wacky!

I do care, James. Deeply. I care because failures of reason irk me. Society works best when people are rational, and rationality works best when people are honest with themselves.

And, be honest, you’ve never pointed to a specific part of the deductive proof of the solution to the Blue Eye problem. You’ve never grappled with the mathematical induction being used. You’ve avoided treating in an intellectually honest way, preferring to mock and hand-wave and declare the discussion over and insinuate a failure of reasoning on the part of anyone who disagrees with you. But none of that changes the validity of the solution. None of that even addresses the solution. The solution to the Blue Eye problem can be shown in many ways, has been shown in many ways, has been analyzed by people much more accomplished in math and logic than you or I and has stood the test of honest and rigorous attempts at defeat. If you think you can defeat it, do so honestly, do so rigorously, do so academically. It would honestly be an accomplishment.

He gave you a bum steer. All his equations are wrong.

Complete strawman.

I don’t believe that one for an instant. You never go to the trouble of looking down that other logic road/option. People who care that they are really right, not merely appearing to be right, go to that trouble. You obstinately avoid it. Either you are hard-hypnotized into being hard-blind to specific concerns, or you simply care more about something else enough to not bother checking out the other option.

Well, at least you know the words … a shame that you don’t care.

Be honest. I pointed to specific reasons why your deduction is irrelevant, not fallacious.
Blued puzzled:
“If everyone is thinking this …”
But what IF they weren’t?

Master Logician Puzzle:
“If we assume that only the colors we see apply, then…”
But what if something else is assumed?

You consistently jump to an easy assumption and go from there, never looking back to verify that your assumption is provable. You just get to an answer and then, apparently in glee, ignore that your starting point was presumptuous. In a courtroom with a jury, that tactic probably would allow an attorney to get away with a great many injustices, as is normal throughout the USA at least. But in a court of logicians, that tactic simply doesn’t fly. Logicians don’t easily forget that your premise assertion was never proven to be necessarily true.

Logicians are not merely jurors.

Bullshit. I had more math in college than you … and then proceeded into engineering, using it.

This is just more of your rhetoric. Great for attorneys in a court of law, not a court of justice.

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Yeah, that is all that I was trying to say. :sunglasses:

Then why do you keep using those equations??? :open_mouth:

Silly question. I had to use them in order to ask if that is what he meant. He is saying something that others are not hearing to mean what he really means to say.

If the change due was 34.56, the cashier gave back 56.34 instead. That’s it in a nutshell. :sunglasses:

You’ll note that none of my syllogisms contain either of these antecedents:

Blue Eye Syllogism 1

Blue Eye Syllogism 2

Master Logician Syllogism 2

I think we all agree with that.

[tab]If e = 34, the received euros, and
c = 56, the received cents then

the proper change (“entitlement”) was said to be
x = c.e => 56.34 => 100c + e, in cents (5634 cents)
x = (100c + e) / 100, in euros
x = c + e/100, in euros

Premise: 2 times the proper change was received plus 5 cents more:
2x + 5, in cents was received.

The received euros is “e” and the received cents is “c”, so:
2x + 5 = e + c, wherein each e = 100 cents and each c = 1 cent

So:
2x + 5 = 100e + c, in cents, or
2x + .05 = e + c/100, in euros

and
x = 100c + e, in cents
x = c + e/100, in euros

thus using merely cents,
2(100c + e) + 5 = 100e + c, in cents
100c + e + 2.5 = 50e + c/2
100c - c/2 = 50e - e - 2.5
c(100 -1/2) = e(50-1) - 2.5
99.5c = 49e - 2.5
c = 49e/99.5 - 2.5/99.5, in cents (thus e must be at least 6)

And then another equation is required to finish it and find x.[/tab]
…edited my booboo.

Yes. Your syllogisms do not because you SKIP OVER the assumptions that you are making. That is why your syllogisms are irrelevant.

You are misstating YOUR presumption as a given premise. Your presumptions are wrong thus your following syllogisms are meaningless.

I gave the correct equation and you turned it around. #-o

This is the answer:
[tab]Let P be the price of book in cents
Let A be the amount of change due from 100 euros in cents
A= 10000 - P

Let R be the returned change in cents

R= 2A + 5

The amount of change due can be represented as E.C
Therefore A and R can be written as:

A= 100E + C
and
R= 100C + E

Substitute these into the previous equation (R=2A+5) and you get :

100C + E = 2(100E + C) + 5
which rearranges to give :
C= (199E + 5)/98

The only value of E which results in an integer value for C is 31
E=31 and C=63

Calculate A and P :
A=3163
P=6837

Price of book was 68.37 in euros.[/tab]

Actually you turned it around in your answer (marked in red). I had defined the e and c in terms of received, not owed (and underlined it several times).

You turned it around by multiplying by 100 in one equation and dividing by 100 in the other. If you define it in terms of cents then both equations would have multiplications by 100.

It was only a matter of defining “e” as what was received versus what was owed.
I defined it as what was received.
You ignored that and redefined as what was due.

That is the only difference (other than me leaving out a later division operation).

You just can’t admit that you make mistakes. :-"

I just did, DS. But my mistakes do not translate into the lack of yours. You screwed up and now can’t admit it.

I have made mistakes in the past and I will make mistakes in the future. :sunglasses:

James, please! Note: Phyllo is right. You have to admit that you made mistakes in the said case.

Okay wake up!

I mentioned the exact mistakes that I made. He denied the ones that he made (possibly still unaware).

Neither of us are claiming to be perfect.

Get your shit straight if you are going to get into the middle.

NOTE!: Phyllo made a mistake in his original complaint because he didn’t realize the definition of “e” that was being discussed. He intruded, unaware of the details. End of that story. He later provided the answer … fine. I have no disagreement with his answer. I provided just short of that answer (trying to not give it all away). In doing that, I made one division error that I pointed out and corrected.

This is NOT an issue of either one of us being egotistical. It is an issue of phyllo not seeing that he had overstepped into an already established discussion (thus redefining the terms). After that point, there was no right and wrong, merely two rights that were different in their nature (due to differently defined terms; specifically “e” and “c”). And then you stepping in, completely blind and making an … of yourself.

Yes. It is okay.

I shall be magnanimous and let James have the pleasure of demonstrating the last part of the solution - calculating E or C from his final equation. O:)