Logic

Ryan$

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Hi guys, I'm so sorry for posting like this question, but I really "confess" don't have iq that much for thinking rightly!

lets assume I arrived to x=y, then I complete my analysis and did some calculations, I arrived to y=z ;
my question in the book given that x=z, why?
I arrived to x=y
y=z, so why x=z?!!!! can someone explain it to me be senseable analogy to our real life to elaborate why if x=y, y=z then x=z ?!

thanks alot
 

Subhotosh Khan

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Hi guys, I'm so sorry for posting like this question, but I really "confess" don't have iq that much for thinking rightly!

lets assume I arrived to x=y, then I complete my analysis and did some calculations, I arrived to y=z ;
my question in the book given that x=z, why?
I arrived to x=y
y=z, so why x=z?!!!! can someone explain it to me be senseable analogy to our real life to elaborate why if x=y, y=z then x=z ?!

thanks alot
Please define x, y & z.

Please also define "=" according to your text book or your understanding.
 

topsquark

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Hi guys, I'm so sorry for posting like this question, but I really "confess" don't have iq that much for thinking rightly!

lets assume I arrived to x=y, then I complete my analysis and did some calculations, I arrived to y=z ;
my question in the book given that x=z, why?
I arrived to x=y
y=z, so why x=z?!!!! can someone explain it to me be senseable analogy to our real life to elaborate why if x=y, y=z then x=z ?!

thanks alot
You have three pots, all with 3 eggs in them. Lable them x, y, z.

The first pot has 3 eggs in it and the second has 3 eggs, so we can write x = y.

The second pot has 3 eggs and the third has three egss, so we can write y = z.

So we know that x = z. Three eggs in x and three eggs in z.

Unless you want to get into axiomatic set theory, that's about as deep as it goes.

-Dan
 

Ryan$

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x,y is variables, "=" is equal like math "=" ..nothing else.
what's struggling me is: yeah x=y right? but who will ensure for me that if I progress in my analysis and arrived to y=z, that's x=y still right? if so then we can say x=z ! but if I didn't change the equation x=y who ensure for me that it's really didn't change that equation and still right for any circumstances ?!

what's confusing me this:
(1) x=y ..so fine with that.
after 5minutes of thinking and analysing problem, I get
(2) y=z

then we conclude that x=z, but what's confusing me why it's that right? who ensures that the first equation is still right and none changed it?! that's what confusing me alot!!!
 

Ryan$

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if I didn't change the equation (1), why would it still right?! who ensure that none touch it and change the equation? I mean yeah x=y, but I went to other calculations while thinking and arrived to equation (2) ! but once again who said that equation (1) still satisfying, yeah I didn't change it ..but who said if I didn't change it, then it's still right for other cases/circumstances I got in progress of my solution?!
 

pka

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Do you think that the transitive relationship is valid?
If so apply it here. If not, why not?
 

JeffM

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if I didn't change the equation (1), why would it still right?! who ensure that none touch it and change the equation? I mean yeah x=y, but I went to other calculations while thinking and arrived to equation (2) ! but once again who said that equation (1) still satisfying, yeah I didn't change it ..but who said if I didn't change it, then it's still right for other cases/circumstances I got in progress of my solution?!
In the context of a specific problem, the meanings of x, y, and z do not change. So if x is the same as y, and z is the same as y, and (for purposes of a given problem) the meanings of x, y, and z do not change, then x and z are also the same.

Remember that variables stand for numbers.

\(\displaystyle 10 + 7 = 20 - 3.\)

\(\displaystyle 33 - 16 = 20 - 3\)

So is it true or false that

\(\displaystyle 10 + 7 = 33 - 16.\)

The statement

\(\displaystyle x = y \text { and } z = y \implies x = z\)

is merely a generalization of that example.
 

Otis

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... my question in the book given that x=z, why?
Is that book written in English? (Maybe that's part of your issue.)

If you and I have exactly $1 in our pocket, and somebody else says to you, "I have exactly $1 in my pocket, just like you", then why think the $1 in my pocket would suddenly change. Magic?

;)
 

Ryan$

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Is that book written in English? (Maybe that's part of your issue.)

If you and I have exactly $1 in our pocket, and somebody else says to you, "I have exactly $1 in my pocket, just like you", then why think the $1 in my pocket would suddenly change. Magic?

;)
I'm totally with you, but in the second part who said that it didn't change?! that's my problem. if I didn't touch your pocket, then is it definitely still the same?!
 

Ryan$

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Is that book written in English? (Maybe that's part of your issue.)

If you and I have exactly $1 in our pocket, and somebody else says to you, "I have exactly $1 in my pocket, just like you", then why think the $1 in my pocket would suddenly change. Magic?

;)
I'm not saying magic, because there's no magic in math. what I'm thinking that none tells that you didn't change what's in your pocket after a while (after we read and finish the second part of your sentence..maybe the first case(your pocket) would be changed ! because a time have passed since we have read your first statement), so how I know that's still $1 in your pocket?!!
 

Denis

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I'm not saying magic, because there's no magic in math. what I'm thinking that none tells that you didn't change what's in your pocket after a while (after we read and finish the second part of your sentence..maybe the first case(your pocket) would be changed ! because a time have passed since we have read your first statement), so how I know that's still $1 in your pocket?!!
Ryan, if I was a moderator, I'd "close" such ridiculous threads....
 

Ryan$

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Ryan, if I was a moderator, I'd "close" such ridiculous threads....
Hi sir, but I'm not joking, if you think I'm joking then why I would open like this thread? because I'm really struggling that and sorry if you have iq of inshtient and I'm not, that's my skills and I'm trying to improve them where's the problem?!!!
 

Ryan$

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Ryan, if I was a moderator, I'd "close" such ridiculous threads....
and instead of just bothering, it could be more than appreciated and honor to help your OP no more nothing else, yeah it might be a silly question, but I face a problem with it which related to me it's magnificent problem, thanks alot
 

Otis

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… who said that [given information] didn't change?! that's my problem …
… maybe the [amount of money in your pocket] changed ! because a time have passed since we have read your first statement …
If any of the dollar amounts (in my example) had changed, then you would have been told, already. So, don't worry about given information changing. Just accept the information in exercises as described.

In your exercise, it's given that x=y and y=z, so those relationships are fixed. Nothing about them is going to change, in that exercise.

If you worry that given information might change, then you won't be able to believe anything! An exercise statement will tell you, if anything changes.

In summary: Do not change given information.

😎
 

Ryan$

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If any of the dollar amounts (in my example) had changed, then you would have been told, already. So, don't worry about given information changing. Just accept the information in exercises as described.

In your exercise, it's given that x=y and y=z, so those relationships are fixed. Nothing about them is going to change, in that exercise.

If you worry that given information might change, then you won't be able to believe anything! An exercise statement will tell you, if anything changes.

In summary: Do not change given information.

😎
thanks alot ! convinced me much appreciated!
 

Ryan$

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To be more clear that who would think that I opened this thread for troll !

I wasn't really known that we can't "simply" change the given information .. I though I could change it because in generally all possibilities would be happen.
thanks you once again to clear out that "DONT CHANGE GIVEN INFORMATION"
 

Denis

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HEY Ryan, if 3 + 2 = 5, then 2 + 3 = ? :)
 

Ryan$

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Denis

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Thing is, we never know what YOUR questions are!
 

Ryan$

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If any of the dollar amounts (in my example) had changed, then you would have been told, already. So, don't worry about given information changing. Just accept the information in exercises as described.

In your exercise, it's given that x=y and y=z, so those relationships are fixed. Nothing about them is going to change, in that exercise.

If you worry that given information might change, then you won't be able to believe anything! An exercise statement will tell you, if anything changes.

In summary: Do not change given information.

😎
Hi otis, pardon me about something to add
then I can say whenever I conclude something or given in the question itself, then it's fixed and there's no real life consequences like if x=6 and we moved to the next statements of the question itself, then if we want to use x, then x=6, there's no possibility that someone could changed it without given any information about ... Yeah?!
 
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