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Why is data in computer science considered to be discrete?
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Problem
I understand that "structure" of data is totally dependent on Boolean Algebra, but:
Why is data considered to be a discrete mathematical entity rather than a continuous one?
Related to this:
What are the drawbacks, or invariants, that are violated in structuring data as a continuous entity in $r$ dimensions?
I am not an expert in the field as I am an undergrad math student, so I'd really appreciate it if someone would explain this to me like I'm five.
Why is data considered to be a discrete mathematical entity rather than a continuous one?
Related to this:
What are the drawbacks, or invariants, that are violated in structuring data as a continuous entity in $r$ dimensions?
I am not an expert in the field as I am an undergrad math student, so I'd really appreciate it if someone would explain this to me like I'm five.
Solution
Answer
why was the data considered to be a discrete mathematical entity rather than a continuous one
This was not a choice; it is theoretically and practically impossible to represent continuous, concrete values in a digital computer, or actually in any kind of calculation.
Note that "discrete" does not mean "integer" or something like that. "discrete" is the opposite of "continuous". This means, to have a computer that is truly able to store non-discrete things, you would need to be able to store two numbers
In mathematics, studying the continuum (i.e., the reals) opens up a lot of fascinating aspects, like measure theory, which makes it utterly impossible to actually store a "continuous" kind of number/data.
why was the data considered to be a discrete mathematical entity rather than a continuous one
This was not a choice; it is theoretically and practically impossible to represent continuous, concrete values in a digital computer, or actually in any kind of calculation.
Note that "discrete" does not mean "integer" or something like that. "discrete" is the opposite of "continuous". This means, to have a computer that is truly able to store non-discrete things, you would need to be able to store two numbers
a and b where `abs(a-b) Heisenberg etc.).In mathematics, studying the continuum (i.e., the reals) opens up a lot of fascinating aspects, like measure theory, which makes it utterly impossible to actually store a "continuous" kind of number/data.
Context
StackExchange Computer Science Q#71648, answer score: 45
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