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Y = Y + 2

Then

Y = Y - 2

Can I go to... 2Y/Y = 2 ?

I can't remember what this belongs to in mathematics...

Thank you for any help.

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closed as not a real question by Austin Mohr, Thomas, Micah, Henry T. Horton, tomasz Dec 12 '12 at 0:38

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

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The statement $Y=Y+2$ is false: if $Y=Y+2$, then $0=2$. It makes sense only as an assignment statement in some programming language, replacing the current value of $Y$ by value $2$ greater. –  Brian M. Scott Dec 11 '12 at 23:13
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From $y=y+2$ you can go to jail, go directly to jail, do not pass Go, do not collect $\$200$. –  Gerry Myerson Dec 11 '12 at 23:14
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The equation $y = y+2$ is true for infinite cardinal numbers $y$. It's also true in characteristic $2$ (because $2=0$ there). –  Robert Israel Dec 11 '12 at 23:15
    
This question is probably asking about recurrence relations. For example, if $Y_{n+1} = Y_n + 2$ then $Y_n = Y_{n+1} - 2$. The subscripts are often omitted when writing computer code; many languages would be happy interpreting the line $y = y+2$ in this way. It's a bummer nobody interpreted it like this... –  Antonio Vargas 15 hours ago

2 Answers 2

up vote 1 down vote accepted

You have written an equation with no solutions: the statement that $Y = Y + 2$ is satisfied by no $Y$. In other words, as a statement, it's false.

In your title, you mention the word "function." A function is something that takes in something, and spits out something else. For example, $f(x) = x + 2$ is a function: if you input $x$, it spits out $x+2$. I've heard people liken functions to machines: you stick stuff in and they crank stuff out.

What you've written is not a function. This also means that it is neither part of the "functions" tag nor the "functional equations" tag - unless you happen to mean that $Y$ is a function of something like $t$. In that case, the statement is still false.

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I've taken the liberty of expunging the offending tags. –  Gerry Myerson Dec 11 '12 at 23:18

This is a false equation. You can go from $Y=Y+2$ to $0=2$

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