• is something subtle about proofing that SQRT(5) < (SQRT(5)+1) ?

    From Nasser M. Abbasi@21:1/5 to All on Sat Oct 30 02:03:28 2021
    since sqrt of number is taken as the positive root, why
    then Maple 2021.1 says it can't show this is true or not? Is
    there something deep I am overlooking here?

    if evalb( 5^(1/2) < (5^(1/2)+1) ) then
    "yes, smaller";
    fi;

    Error, cannot determine if this expression is true or false: 5^(1/2) < 5^(1/2)+1

    if 5^(1/2) < (5^(1/2)+1) then
    "yes, smaller";
    fi;

    Error, cannot determine if this expression is true or false: 5^(1/2) < 5^(1/2)+1

    But in Mathematica it did not complain

    5^(1/2) < (5^(1/2) + 1)
    True

    This is very strange. Does your CAS have any problem showing
    that 5^(1/2) is smaller than 5^(1/2)+1?

    In Maple, it can do it if I convert everything to float

    if evalf(5^(1/2)) < evalf((5^(1/2)+1)) then
    "yes, smaller";
    fi;

    "yes, smaller"

    --Nasser

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  • From acer@21:1/5 to Nasser M. Abbasi on Sat Oct 30 06:03:42 2021
    On Saturday, October 30, 2021 at 3:03:32 AM UTC-4, Nasser M. Abbasi wrote:
    since sqrt of number is taken as the positive root, why
    then Maple 2021.1 says it can't show this is true or not? Is
    there something deep I am overlooking here?

    if evalb( 5^(1/2) < (5^(1/2)+1) ) then
    "yes, smaller";
    fi;

    Error, cannot determine if this expression is true or false: 5^(1/2) < 5^(1/2)+1

    if 5^(1/2) < (5^(1/2)+1) then
    "yes, smaller";
    fi;

    Error, cannot determine if this expression is true or false: 5^(1/2) < 5^(1/2)+1

    But in Mathematica it did not complain

    5^(1/2) < (5^(1/2) + 1)
    True

    This is very strange. Does your CAS have any problem showing
    that 5^(1/2) is smaller than 5^(1/2)+1?

    In Maple, it can do it if I convert everything to float

    if evalf(5^(1/2)) < evalf((5^(1/2)+1)) then
    "yes, smaller";
    fi;

    "yes, smaller"

    --Nasser

    You are simply using the wrong command, `evalb`, instead of an appropriate command such as `is`.

    evalb( 5^(1/2) < (5^(1/2)+1) );
    1/2 1/2
    5 < 5 + 1

    is( 5^(1/2) < (5^(1/2)+1) );
    true

    Your incorrect preconceptions as to the designed functionality of the `evalb` command are getting in your way here.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From acer@21:1/5 to acer on Sat Oct 30 08:53:49 2021
    On Saturday, October 30, 2021 at 9:03:43 AM UTC-4, acer wrote:
    On Saturday, October 30, 2021 at 3:03:32 AM UTC-4, Nasser M. Abbasi wrote:
    since sqrt of number is taken as the positive root, why
    then Maple 2021.1 says it can't show this is true or not? Is
    there something deep I am overlooking here?

    if evalb( 5^(1/2) < (5^(1/2)+1) ) then
    "yes, smaller";
    fi;

    Error, cannot determine if this expression is true or false: 5^(1/2) < 5^(1/2)+1

    if 5^(1/2) < (5^(1/2)+1) then
    "yes, smaller";
    fi;

    Error, cannot determine if this expression is true or false: 5^(1/2) < 5^(1/2)+1

    But in Mathematica it did not complain

    5^(1/2) < (5^(1/2) + 1)
    True

    This is very strange. Does your CAS have any problem showing
    that 5^(1/2) is smaller than 5^(1/2)+1?

    In Maple, it can do it if I convert everything to float

    if evalf(5^(1/2)) < evalf((5^(1/2)+1)) then
    "yes, smaller";
    fi;

    "yes, smaller"

    --Nasser
    You are simply using the wrong command, `evalb`, instead of an appropriate command such as `is`.

    evalb( 5^(1/2) < (5^(1/2)+1) );
    1/2 1/2
    5 < 5 + 1

    is( 5^(1/2) < (5^(1/2)+1) );
    true

    Your incorrect preconceptions as to the designed functionality of the `evalb` command are getting in your way here.

    I could add that the functionality changes according to the `type` of the input, for a clear programmatic distinction.

    The `evalb` command tests an inequality if the arguments are of type `numeric`, in Maple's technical sense of the `type` command. And that type does not include exact radicals (though it does include, say, rationals and floats).

    For strict equality testing the functionality is also according to that same `numeric` type. But in this case the remaining cases are subjested to a pure address check (which is a structural rather than a mathematical comparison).

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    * Origin: fsxNet Usenet Gateway (21:1/5)