Zero to the zeroth power

Hodorious shared this problem 7 years ago

Not a Problem

GeoGebra evaluates 0^0 to 1, which is not correct, or at least there is no consensus on this. Moreover, when you try to raise zero to a negative power, the program just outputs infinity. 0^0 is evaluated to 1 in the Algebra and Spreadsheet view. In CAS, 0^0 just returns a question mark, so there's also a lack of consistency.

Was this intended to work like this?

Using GeoGebra 5.0.266.0

The same problem

Comments (9)

Michael Borcherds ● 7 years ago

Yes, that's intended

Reply URL

Jozef Dobos ● 4 years ago

In CAS:

0^0 returns a question markIsDefined(0^0) returns true

Why?

Reply URL

Michael Borcherds ● 4 years ago

IsDefined() isn't implemented in the CAS (although by coincidence it will be for next release :) )

URL

Michael Borcherds ● 4 years ago

https://help.geogebra.org/t...

Reply URL

Jozef Dobos ● 4 years ago

http://www.askamathematicia...

Files: 0^0.jpg

Reply URL

Michael Borcherds ● 3 years ago

https://www.geogebra.org/m/rmcxa9un

Reply URL

Jozef Dobos ● 3 years ago

Of course, I know that. However, in reality it is just a form of notation.

Instead of Sum(Sequence(x^i/i!,i,0,n)), it is sufficient to write

1+Sum(Sequence(x^i/i!,i,1,n)), or Sum(Sequence(If(i>0,x^i,1)/i!,i,0,n)).

To define 0^0 is useful for programmers but it might not be suitable for

teachers of mathematics. GeoGebra seems to have sometimes forgotten about high-school mathematics, the pupils and their teachers. I looked into several textbooks that I have at hand and each of them deals with the topic of Zero and Negative Integer Exponents, but neither defines the expression 0^0.

Here is the list of textbooks:

Aufmann, R. N., Lockwood, J. S.: Introductory Algebra. An Applied Approach, 2010.

Aufmann, R. N., Barker, V. C., Nation, R. D.: College Algebra and Trigonometry, 2011.

Axler, S.: Algebra and Trigonometry, 2012.

Baratto, S., Bergman, B., Hutchinson, D.: Elementary and Intermediate Algebra, 2010.

Barnett, R. A., Ziegler, M. R., Byleen, K. E., Sobecki, D.: College Algebra, 2011.

Barnett, R. A., Ziegler, M. R., Byleen, K. E.: Colege Mathematics for Business, Econonics, Life Sciences, and Social Sciences, 2015.

Barnett, R. A., Ziegler, M. R., Byleen, K. E.: Precalculus, Functions and Graphs, 2001.

Barnett, R. A., Ziegler, M. R., Byleen, K. E., Sobecki, D.: Precalculus: Graphs and Models, 2009.

Beecher, J. A., Penna, J. A., Bittinger, M. L.: Algebra and Trigonometry, 2012.

Beleznay, F.: Mathematics for the IB Diploma, 2016.

Bello, I.: Introductory Algebra, A Real World Approach, 2009.

Bettinger, A. K., Englund, J. A.: Algebra and Trigonometry, 1963.

Bittinger, M. L., Ellenbogen D. J., Johnson, B. L.: Elementary and Intermediate Algebra: Graphs and Models, 2012.

Blitzer, R.: College Algebra, 2004.

Brown, S. A., Breunlin, R. J., Wiltjer, M. H.: UCSMP Algebra, 2004.

Cohen, D.: Precalculus, A Problem-Oriented Approach, 2005.

Crisler, N., Simundza, G.: Modeling with Mathematics, A Bridge to Algebra II, 2012.

Dugopolski, M.: Elementary and Intermediate Algebra, 2012.

Gantert, A. X.: Algebra 2 and Trigonometry, 2009.

Martin-Gay, K. E.: Algebra, A Combined Approach, 2012.

Martin-Gay, K. E., Greene, M.: Intermediate Algebra, A Graphing Approach, 2014.

McGraw-Hill authors: IMPACT Mathematics: Algebra and More, Course 3, Student Edition, 2005.

Gloag, A., Gloag, A., Kramer, M., Introductory Algebra, CK-12 Foundation, 2012.

Gustafson, R. D., Hughes, J. D.: College Algebra, 2013.

Holliday, B., Luchin, B., Cuevas, G. J., Carter, J. A., Marks, D., Day, R., Casey,R. M., Hayek, L. M.: Algebra 2, 2008.

Schultz, J. E., Ellis, W., Hollowell, K. A., Kennedy, P. A.: Algebra 2, 2004.

Hornsby, J., Lial, M. L. Rockswold, G.: A Graphical Approach to College Algebra, 2015.

Kaufmann, J. E., Schwitters, K. L.: Algebra for College Students, 2011.

Kaufmann, J. E., Schwitters, K. L.: College Algebra, 2004.

Kime, L. A., Clark, J., Michael, B. K.: Explorations in College Algebra, 2007.

Larson, R., Hostetler, R., Kelley, P. M.: Intermediate Algebra, 2008.

Larson, R., Falvo, D. C.: Algebra and Trigonometry, 2011.

Larson, R., Hodgkins, A. V.: College Algebra with Applications for Business and the Life Sciences, 2009.

Larson, R., Boswell, L., Kanold, T. D., Sti, L., Algebra 1. Concepts and Skills, 2004.

Larson, R., Boswell, L., Kanold, T. D., Sti, L., Algebra 1, 2004.

Lehmann, J.: Elementary Algebra, Graphs and Authentic Applications, 2015.

Malloy, C. E., Molix-Bailey, R. J., Price, J., Willard, T.: Pre-Algebra, 2008.

McCallum, W. G., Connally, E., Hughes-Hallet, D., et al.: Algebra, Form and Function, 2010.

McCune, S. L.: Algebra I, Review and Workbook, 2019.

Murdock, J., Kamischke, E., Kamischke, E.: Discovering Algebra, An Invstigative Approach, 2007.

Narasimhan, R.: Precalculus, Building Concepts and Connections, 2009.

Coene, C., LeBlanc, D., Edwards, B., Sherk, R. et al.: Foundations for College Mathematics, 2009.

Stewart, J., Redlin, L., Watson, S.: Precalculus, Mathematics for Calculus, 2009.

Sultan, A., Atrzt, A. F.: The Mathematics That Every Secondary Scholl Math TeacherNeeds to Know, 2018.

Swokowksi, E. W., Cole, J. A.: Algebra and Trigonometry with Analytic Geometry, 2008.

Tussy, A. S., Gustafson, R. D.: Developmental Mathematics for College Students, 2006.

Tussy, A. S., Gustafson, R. D., Koenig, D. R.: Intermdiate Algebra, 2011.

Tussy, A. S., Gustafson, R. D.: Intermdiate Algebra, 2013.

Coburn, J. W., Herdlick, J. D.: College Algebra, Graphs and Models, 2012.

Charles, R. I., Hall, B., Kennedy, D., Bellman, A. E. et al.: Algebra 1, Common Core, 2015.

URL

Michael Borcherds ● 3 years ago

neither defines the expression 0^0.

So will you write to the authors so they can correct their next editions?

1 used to be considered prime, now it's not. It's just a matter of convention, same with 0^0. I used to think the same as you but it's simply more pragmatic to define 0^0=1

URL

mathmagic ● 3 years ago

otro ejemplo. A mí me gusta que funcione

aunque a o b o c sean cero

/Afl7aREChMEvAAAAAElFTkSuQmCC

Reply URL