According to my professor, there exist infinite dimensional vector spaces without a basis, and he asked us to find one. But isn't this impossible? The definition of a dimension is the number of elements in the basis of the vector space. So if the space is infinite-dimensional, then the basis of that space has an infinite amount of elements..(adsbygoogle = window.adsbygoogle || []).push({});

the only vector space I can think of without a basis is the zero vector...but this is not infinite dimensional..

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# Infinite dimensional vector spaces without basis?

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