# Logic

##### Full Member
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

##### Super Moderator
Staff member
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.

• topsquark

#### topsquark

##### Full Member
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

##### Full Member
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

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

• topsquark

#### JeffM

##### Elite Member
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.

• topsquark

#### Otis

##### Elite Member
... 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 $1 in my pocket would suddenly change. Magic? #### Ryan$

##### Full Member
Hi guys ! I'm so sorry for posting over here like this question, but I don't understand yet the "equal": "=" in math

what's confusing me, why if x=y then we can assign instead of x, y or actually instead of y x ..why is that correct?! may please anyone explain to me what "=" means by an analogy to be more sensitive to me?!

#### JeffM

##### Elite Member
When we say $$\displaystyle x = y$$,

we mean that x and y represent the same thing. They are just different names for the same thing. If you own only one dog and it is named Toto, it makes no difference whether you say "my dog" or "Toto" because both refer to the same animal.

By "same thing" in math, we frequently mean "have the same numerical value."

So I can say $$\displaystyle 13 + 3 = 21 - 5$$

because both expressions evaluate to the same result, namely 16.

You seem to be taking something that is easy and making it hard. In the case of 13 + 3 and 21 - 5, the expressions themselves are different, but the value of the expressions is identical. We look beyond the superficial form of the expressions and consider the quantitative meaning represented by the expressions.

So yes we can replace 13 + 3 by 21 - 5 or replace 21 - 5 by 13 + 3 because both expressions are quantitatively identical.

• Ryan$, HallsofIvy and topsquark #### Ryan$

##### Full Member
When we say $$\displaystyle x = y$$,

we mean that x and y represent the same thing. They are just different names for the same thing. If you own only one dog and it is named Toto, it makes no difference whether you say "my dog" or "Toto" because both refer to the same animal.

By "same thing" in math, we frequently mean "have the same numerical value."

So I can say $$\displaystyle 13 + 3 = 21 - 5$$

because both expressions evaluate to the same result, namely 16.

You seem to be taking something that is easy and making it hard. In the case of 13 + 3 and 21 - 5, the expressions themselves are different, but the value of the expressions is identical. We look beyond the superficial form of the expressions and consider the quantitative meaning represented by the expressions.

So yes we can replace 13 + 3 by 21 - 5 or replace 21 - 5 by 13 + 3 because both expressions are quantitatively identical.
I got you !
but lemme ask something else, if I assign "my dog"=z , then we can call "my dog" as z?! what's confusing me, we must define "my dog" =: z and not "my dog" = z ! there's difference between "=" and "=:"(definition in math) .. but it seems the same ? I mean the mean of "=" is the same as "=:" ?!

#### Ryan\$

##### Full Member
Are you talking about equality vs assignment?
well what's confusing me is how can I do x=y and then say that's y is the same as x, but I didn't before define what's y !

#### lev888

##### Senior Member
Could you post an example of a problem that involves the issue that's confusing you? Otherwise it's very hard to understand you.

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