How do calculators have answers for every equation?
In: Mathematics
I’m assuming you’re thinking about a pocket calculator [like this](https://en.wikipedia.org/wiki/TI-30#/media/File:TI-30X_SOLAR,_2.jpg). It doesn’t deal with *equations* at all (what you ask about in your question). It only deals with *expressions* that don’t involve variables.
All the operations (calculator buttons) are things that can be calculated from known variables. If you remember how to add or multiply numbers with pencil and paper, you should realize the step-by-step process [1] can be applied to *any* number regardless of how many digits it has. To add numbers, the hardware and software inside the calculator (which is really a tiny computer) uses the same paper-and-pencil algorithm you would to add them.
More “advanced” buttons like square root, `cos()` or `ln()` also have algorithms which allow them to be calculated. The algorithms are just more complicated.
[1] Mathematicians and computer scientists call a step-by-step process an *algorithm*.
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