Comment on Goodsteins theoremparentComments−H8crilA2yExcessive power has been proven to be just addition and multiplication over the natural numbers. So - no, we can't.−naasking2yYes, addition and multiplication over the infinite naturals. I don't think it's obvious that all three of these are needed together for all interesting applications. For instance, various types of finitism eliminate the infinities.
Comments
Excessive power has been proven to be just addition and multiplication over the natural numbers. So - no, we can't.
Yes, addition and multiplication over the infinite naturals. I don't think it's obvious that all three of these are needed together for all interesting applications. For instance, various types of finitism eliminate the infinities.