Can we consider equations as functions?

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The discussion centers on whether equations can be classified as functions, specifically examining the equation f(x) = 4x + 1. Participants express differing opinions, with some asserting that equations represent functions while others argue they are not functions themselves. The consensus leans towards accepting f(x) = 4x + 1 as a function for practical purposes, despite the semantic debate surrounding the definitions. The argument highlights the distinction between set-theoretic definitions and practical applications in mathematics.

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A function is defined as a set of ordered-pairs where ...

But can we consider equations as functions?

Some says 'yes'.

Some says 'no', because according to them, equations are not actually functions. They are just used to define/represent functions.

example: y=4x+1/f(x)=4x+1.
Can we consider this as a function? Or, it is just an equation that defines/represents a function?

Thank you!
 
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It really depends on the context. For most non set-theoretic purposes, saying the function f(x)=4x+1 is perfectly fine. Especially since the definition of a function as a set of ordered pairs is only developed for the use of studying functions in a set theoretic setting
 


The people who respond "no" are being kind of ridiculous. I care very little for semantics when it contributes really nothing at all. Yes, of course f(x) = 4x + 1 is a function, or else why would we have gone through the trouble of creating the modern definition at all.
 

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