# Logic

#### lev888

##### Full Member
Again, an example would help.
There are areas of math where problems have variables that do change. But it's clear from the problem statement which variables change and which don't. E.g. a diver steps off the diving platform that is 5 meters high. If the initial speed is 0 m/sec what will be his speed when he touches the water? Here the speed is 0 m/sec initially, but we know from observing falling apples that it increases based on certain laws of physics. But the platform height stays the same - we can assume that while the diver is in the air nobody drained the pool.

##### Full Member
Also can I say that same means "doesn't matter which once to use of the two equal variables, they are the same" ?!

#### lev888

##### Full Member
Also can I say that same means "doesn't matter which once to use of the two equal variables, they are the same" ?!
Once again, example would help.

x = y means the 2 variables have the same value.

#### HallsofIvy

##### Elite Member
"x= y" means that "x" and "y" are two symbols both representing the same number ("same" here having its usual English meaning). Some times you will see "same" used to mean that two things are "equivalent" under a previously define equivalence relation.

#### JeffM

##### Elite Member
We have said before that what "same" means depends on context. In elementary algebra, it generally means that two sets of symbols represent the same numeric value.

$$\displaystyle 3 + 7 = (2 * 9) - 8.$$

In other branches of mathematics, it may have a different meaning

$$\displaystyle f'(x) = g'(x)$$

means that two functions have equivalent derivatives, which are functions rather than numbers.

What it always means, however, is that you can replace what is on one side of the equality with what is on the other whenever that is convenient.

And whatever do you mean by "cosmetics?" The primary meaning of that word refers to things like lipstick and fingernail polish.

#### Otis

##### Senior Member
… whenever I conclude something or [it's] given … then it's fixed and there's no real life consequences …
I can't say that applies to all parts of every math exercise, but -- in general -- the given conditions of an exercise don't change.

And, yes, if you're told that x=6 for some specific purpose, then x is 6 for that purpose and you don't need to consider that 6 might change into a different number in that part of the exercise.

I agree with lev888, above. When you feel uncertain about something in an exercise, I think you need to post the complete exercise statement verbatim, and then tell us what you're thinking. When you ask questions by making up bits and pieces of unrelated stuff as examples, it puts us in the position of trying to generalize about situations we can't see. There are exceptions in math, so I think working with a specific, complete exercise statement is the best way to deal with your concerns.

##### Full Member
what I'm asking about is, can we take the "conclusions logic" of specific equation(that's given in advance) as a given information?!

#### JeffM

##### Elite Member
Hi guys! once again I'm sorry for posting like those question, but I really not succeeding solving those gaps by myself and thanks alot.

My problem is like this, lets assume that's x=y=z , then we conclude x=z ! it's really fine but it's a conclusion and not given data.
so now if I do z+m= 5, can I assign instead of z, x? I mean to write x+m=5 ?! what's confusing me because we conclude that x=z but it's not given information, given x=y=z, and from this we conclude x=z so I'm asking can I depend also on my implicitly conclusion of the given data(x=y=z) ?! thanks alot !
Your questions border on the incoherent.

You start with the GIVEN data that x = y = z. (Actually that is sloppy and confusing because equality is a binary relation. So what you really mean is "GIVEN x = y and y = z.")

Yes, you are ABSOLUTELY correct that we are not told that x = z. Instead, we have an axiom that says

$$\displaystyle x = y \text { and } y = z \implies x = z.$$

It is not something that we must derive. It is an axiom that we are allowed to use without proof. It is a generalization of this example.

$$\displaystyle 3 + 8 = 11 \text { and } 11 = 17 - 6 \implies 3 + 8 = 17 - 6.$$

You can demonstrate physically the above example. Standard mathematics generalizes from that example and many similar examples to say that, in all cases,

$$\displaystyle x = y \text { and } y = z \implies x = z.$$

Now if you want, you can build a NON-STANDARD mathematics that denies that axiom, but I doubt it will be very useful when applied to the real world.

#### Otis

##### Senior Member
… lets assume … x=y=z …

… we conclude that x=z but it's not given …
That's correct. It's not given because you assumed it.

Nobody here knows what is given, until you post a complete exercise statement.

#### Ryan$##### Full Member Hi guys, I'm really struggling something which I couldn't find a solution for it! I always going to negatively what result I get. I mean, lets assume I get from equation logic that x=2y. so " I " can assume x != 2y (not equal) .. why not? while the logic is giving me opportunity to do whatever things in general why not claiming that assumption?! I can think in general and one of possibilities of general is x != 2y .. so it's possible ! Last edited by a moderator: #### JeffM ##### Elite Member Yes, you may make up any mathematics you want. In your mathematics, $$\displaystyle 6 = 2 * 3 \implies 6 \ne 2 * 3.$$ I understand. Unfortunately, we do not answer questions about Ryan-math. You will have to ask Ryan about it. #### tkhunny ##### Moderator Staff member 3 = 5 - False 4 = 4 - True x = 2y - Conditionally True. One must pick x and y that work. #### Otis ##### Senior Member … I always going to negatively what result I get … I don't understand what you mean. Please post the complete exercise statement. #### JeffM ##### Elite Member I don't understand what you mean. Please post the complete exercise statement. There is no exercise statement. He is trying to find ways to contradict basic axioms. #### pka ##### Elite Member There is no exercise statement. He is trying to find ways to contradict basic axioms. I am very reluctant to call names. But Ryan$ takes the cake S/he is by any means of the imagination an InterNet TROLL.
Please, please follow that LINK. If anyone can argue that Ryan$fails to fulfill that definition of a TROLL please post your justifications. In the absent of any cogent defense I ask that Ryan$ be banded.

#### Otis

##### Senior Member
… If anyone can argue that Ryan$fails to fulfill that definition of a TROLL please post your justifications … Ryan$ has the mind of a child.

… from equation logic … x=2y …
… logic [lets me] do whatever …
… I can think in general … so it's possible [that x≠2y]