- #1
lLovePhysics
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How is y=0 an odd function when it isn't symmetric to the origin?
Is y=0 an Odd Function Despite Not Being Symmetric About the Origin?
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Homework Help Overview
The discussion centers around the classification of the function y=0 in terms of odd and even functions, particularly questioning its symmetry properties.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the definition of odd functions and whether y=0 fits this definition despite its lack of symmetry about the origin. There are also discussions about the nature of functions being odd, even, or both.
Discussion Status
Some participants provide insights into the definitions of odd and even functions, while others clarify potential misunderstandings regarding terminology. The conversation reflects a mix of interpretations and attempts to reconcile different concepts.
Contextual Notes
There is a noted confusion between the terms "odd" and "even" versus "open" and "closed," which may affect the clarity of the discussion. Participants are also reflecting on their understanding of function properties in a broader mathematical context.
- #2
benorin
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Sure it is. Consider f(x)=0 and recall the definition of an odd function.
- #3
CompuChip
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Note here, that for any function f in general, it's not necessary that f is either odd or even; nor that it cannot be both. You've found an example of the latter 
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HallsofIvy
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Did you mean "odd" and "even"? f(x)= 0 is clearly a closed function, certainly not open!CompuChip said:Note here, that for any function f in general, it's not necessary that f is either closed or open; nor that it cannot be both. You've found an example of the latter
It is definitely both even and odd.
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CompuChip
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Heh, just read a topology thread. I was thinking "odd" and "even", but I wrote "open" and "closed". Still a bit sleepy probably :O
I'll change my post
I'll change my post
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