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The base argument to int is meant to be used when parsing a string, not when passing an int to int :

>>> int('ff', 16)
It's a well-established convention to use a, b, c, ..., z for digits representing 10, 11, 12, ..., 35, but there's no convention for what symbol to use for digit 36 in base 37.
First of all: you can only specify a base for int() when converting strings into numbers. Say you have a string with a hexadecimal number, so base 16:
>>> int('2a', 16)
This result differs significantly from the same string interpreted as a different base:
>>> int('2a', 11)
>>> int('2a', 29)
You only ever need the base of an integer number when presenting the value visually or when parsing the integer value from a string representation. You can display an integer value in many different ways, but an int object is the value, not a visual presentations, and doesn't have a base nor can you change that base.
The logical extension when already supporting hexadecimal notation (digits 0-9 and letters A-F), is also support using the letters G-Z, and 10 digits and 26 letters makes it possible to use base 36:
>>> int('zz', 36)
Further bases would need to use non-alphanumeric symbols, for which there is no clear pre-set ordering.
You can't have a base lower than 2; you can't count with just a single digit, the value of 0 will not change.
                thanks for explanation, as mathematically it is possible to encode high value, was confused why it's limited here in python.
– sahasrara62
                Jan 18, 2019 at 18:18
This is a practical implementation convention.  What do you envision as the character set for base 100?  :-)
Using digits and the entire alphabet is common enough, so the base function with a contiguous set of acceptable base values implemented the functionality that far.  Base 1 is simply len(arg).
There is also a convention for base-64 encoding; without a convention for the values 37-63, though, the base function left the radix-64 value for a separate interface.
                The base64 encoding conventions (plural!) are incompatible with the usual mapping of symbols to digits, too - for example, the symbol '0' doesn't represent the value 0 in base64 encoding.
– user2357112
                Jan 18, 2019 at 17:58
                Right -- that wouldn't keep base from making the conversion, but the functionality would not be smooth over an apparently small parameter change.
– Prune
                Jan 18, 2019 at 18:13
                @Prune i was just experimenting it out . as mathematically it's possible to encode it this high, was checking that in python whether this is possible or not.
– sahasrara62
                Jan 18, 2019 at 18:16
                Of course.  It's certainly possible -- but you need to have a convention for the textual representation.  There's an obvious interpretation if the input text is limited to the 36 or 64 characters already accepted.  However, since we do not have a convention for the other characters in an arbitrarily long set, the built-in functions don't support those bases.  Writing your own is easy, if you want that functionality.
– Prune
                Jan 18, 2019 at 18:19
        
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