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"

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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"

Hi , is that relevant to my question tho?HEY Ryan, if 3 + 2 = 5, then 2 + 3 = ?

5

Hi otis, pardon me about something to addIf 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'sgiventhat 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 believeanything! An exercise statement will tell you, if anything changes.

In summary:Do not change given information.

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?!

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.

I mean, once we have two things are equal, x=y for example, then we say that x is the same as y or vice versa, what's confusing me what do we intend once we said "the same" ? I know it's simple logic but if my simple logic sucks, then I can't complete learning, and by you guys I believe that I will close those gaps.

I define the same is: two things the same regardless to its cosmetics, I mean regardless to what we call the variables, if they are referring to the same object then they are the "same" .. is this a good enough explanation to define what same is?

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

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

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

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.

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I can't say that applies to… whenever I conclude something or [it's] given … then it's fixed and there's no real life consequences …

And, yes, if you're told that x=6 for some specific purpose, then x

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

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.

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 !

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

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

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.

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That's correct. It's not given because you assumed it.… lets assume … x=y=z …

… we conclude that x=z but it's not given …

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

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 !

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 !

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I don't understand what you mean.… I always going to negatively what result I get …

Please post the complete exercise statement.