the term "same" in math

Ryan$

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Jan 25, 2019
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Hi guys, may please anyone in its explanation explain to me what does "the same" means in math?
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?
 

Ryan$

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Jan 25, 2019
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Also can I say that same means "doesn't matter which once to use of the two equal variables, they are the same" ?!
 

lev888

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Jan 16, 2018
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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

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Jan 27, 2012
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"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

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Sep 14, 2012
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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.
 
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