Can we consider equations as functions?

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The discussion centers on whether equations can be considered functions, with opinions divided. Some argue that equations like y=4x+1 or f(x)=4x+1 are indeed functions, while others contend that they merely represent functions. The context of use is emphasized, suggesting that for practical purposes, referring to f(x)=4x+1 as a function is acceptable. Critics of the opposing view are described as overly focused on semantics. Ultimately, the consensus leans towards recognizing equations as functions in most contexts.
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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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