Jensen Inequality - without calculus please

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Could someone please explain to me what is Jensen Inequality about, without calculus? I know basically what are convex and concave functions - about their positioning in the Cartesian Plane - but I have not found until this day any type of material about Jensen Inequality without the use of calculus.




inequality




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  • 1




    The wikipedia page doesn't use any calculus to explain it...
    – Bernard W
    Jul 18 at 1:35






  • 2




    There is a finite form of Jensen's inequality which doesn't require calculus, and is explained on the Wikipedia page. The general form is a theorem in calculus, and obviously can't be explained, or even understood, without calculus. Stick to the finite form, and you should be ok.
    – saulspatz
    Jul 18 at 2:03










  • I was reluctant to trust in Wikipedia, since I´ve found some errors in mathematics articles on Wikipedia to this day. Thank you, though!
    – Elizabeth Middleford
    Jul 18 at 15:01














up vote
0
down vote

favorite












Could someone please explain to me what is Jensen Inequality about, without calculus? I know basically what are convex and concave functions - about their positioning in the Cartesian Plane - but I have not found until this day any type of material about Jensen Inequality without the use of calculus.




inequality




share|cite|improve this question















  • 1




    The wikipedia page doesn't use any calculus to explain it...
    – Bernard W
    Jul 18 at 1:35






  • 2




    There is a finite form of Jensen's inequality which doesn't require calculus, and is explained on the Wikipedia page. The general form is a theorem in calculus, and obviously can't be explained, or even understood, without calculus. Stick to the finite form, and you should be ok.
    – saulspatz
    Jul 18 at 2:03










  • I was reluctant to trust in Wikipedia, since I´ve found some errors in mathematics articles on Wikipedia to this day. Thank you, though!
    – Elizabeth Middleford
    Jul 18 at 15:01












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Could someone please explain to me what is Jensen Inequality about, without calculus? I know basically what are convex and concave functions - about their positioning in the Cartesian Plane - but I have not found until this day any type of material about Jensen Inequality without the use of calculus.




inequality




share|cite|improve this question











Could someone please explain to me what is Jensen Inequality about, without calculus? I know basically what are convex and concave functions - about their positioning in the Cartesian Plane - but I have not found until this day any type of material about Jensen Inequality without the use of calculus.





inequality





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 18 at 1:32









Elizabeth Middleford

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  • 1




    The wikipedia page doesn't use any calculus to explain it...
    – Bernard W
    Jul 18 at 1:35






  • 2




    There is a finite form of Jensen's inequality which doesn't require calculus, and is explained on the Wikipedia page. The general form is a theorem in calculus, and obviously can't be explained, or even understood, without calculus. Stick to the finite form, and you should be ok.
    – saulspatz
    Jul 18 at 2:03










  • I was reluctant to trust in Wikipedia, since I´ve found some errors in mathematics articles on Wikipedia to this day. Thank you, though!
    – Elizabeth Middleford
    Jul 18 at 15:01












  • 1




    The wikipedia page doesn't use any calculus to explain it...
    – Bernard W
    Jul 18 at 1:35






  • 2




    There is a finite form of Jensen's inequality which doesn't require calculus, and is explained on the Wikipedia page. The general form is a theorem in calculus, and obviously can't be explained, or even understood, without calculus. Stick to the finite form, and you should be ok.
    – saulspatz
    Jul 18 at 2:03










  • I was reluctant to trust in Wikipedia, since I´ve found some errors in mathematics articles on Wikipedia to this day. Thank you, though!
    – Elizabeth Middleford
    Jul 18 at 15:01







1




1




The wikipedia page doesn't use any calculus to explain it...
– Bernard W
Jul 18 at 1:35




The wikipedia page doesn't use any calculus to explain it...
– Bernard W
Jul 18 at 1:35




2




2




There is a finite form of Jensen's inequality which doesn't require calculus, and is explained on the Wikipedia page. The general form is a theorem in calculus, and obviously can't be explained, or even understood, without calculus. Stick to the finite form, and you should be ok.
– saulspatz
Jul 18 at 2:03




There is a finite form of Jensen's inequality which doesn't require calculus, and is explained on the Wikipedia page. The general form is a theorem in calculus, and obviously can't be explained, or even understood, without calculus. Stick to the finite form, and you should be ok.
– saulspatz
Jul 18 at 2:03












I was reluctant to trust in Wikipedia, since I´ve found some errors in mathematics articles on Wikipedia to this day. Thank you, though!
– Elizabeth Middleford
Jul 18 at 15:01




I was reluctant to trust in Wikipedia, since I´ve found some errors in mathematics articles on Wikipedia to this day. Thank you, though!
– Elizabeth Middleford
Jul 18 at 15:01















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