CAS: log of large integers?

[Joe Horn]

(05-23-2015 06:23 PM)DrD Wrote:  What exactly is an exact integer?

It's a specific object type in the Prime and HP 49/50 series calculators, namely, an integer whose number of digits is limited only by available memory. For example, if you do 2^63 on the HP 49/50 in exact mode, or on the Prime in CAS view (with its Exact mode set), you get the exact integer result of 9223372036854775808. If you perform the same calculation on the 49/50 in approximate mode, or on the Prime in Home view, you only get the approximate answer of 9.22337203685ᴇ18 which shows how standard HP reals have mantissas with at most 12 digits.

(05-23-2015 06:23 PM)DrD Wrote:  A whole number, positive, negative or 0? A number without fraction? Then are -1.0, 0.0, or 1.0 exact integers, or are they inexact integers?

They CAN be integers, but they are not necessarily. The dead giveaway is the absence of a decimal point in CAS (or on the HP 49/59 in exact mode). If you add 1+2 and get "3" (no decimal point) then it's an integer, but if you get "3." then it's a real, not an integer.

Prolepsis: Yes, of COURSE it's mathematically an integer. But that's not what we're talking about. We're talking about calculator object types here, not mathematical entities. Sorry if that was unclear.