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Dirk
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Sometimes it makes a lot of sense to state two different theorems even if one is a special case if the other, e.g. when the special case has a considerableconsiderably simpler proof (some things hold in Banach spaces and, consequently, in Hilbert spaces as well, but in Hilbert spaces the proof may much simpler, e.g. proving that the unit ball is weakly sequentially compact).

Also, there may be historic reasons. Finally, I have a vague feeling that a "theorem" is more than just the statement of the assertion. The same theorem may come in different versions, sometimes equivalent, sometimes slightly different, but they all present a general more abstract idea.

Sometimes it makes sense to state two different theorems even if one is a special case if the other, e.g. when the special case has a considerable simpler proof (some things hold in Banach spaces and, consequently, in Hilbert spaces as well, but in Hilbert spaces the proof may much simpler).

Also, there may be historic reasons. Finally, I have a vague feeling that a "theorem" is more than just the statement of the assertion. The same theorem may come in different versions, sometimes equivalent, sometimes slightly different, but they all present a general more abstract idea.

Sometimes it makes a lot of sense to state two different theorems even if one is a special case if the other, e.g. when the special case has a considerably simpler proof (some things hold in Banach spaces and, consequently, in Hilbert spaces as well, but in Hilbert spaces the proof may much simpler, e.g. proving that the unit ball is weakly sequentially compact).

Also, there may be historic reasons. Finally, I have a vague feeling that a "theorem" is more than just the statement of the assertion. The same theorem may come in different versions, sometimes equivalent, sometimes slightly different, but they all present a general more abstract idea.

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Dirk
  • 12.7k
  • 6
  • 54
  • 97

Sometimes it makes sense to state two different theorems even if one is a special case if the other, e.g. when the special case has a considerable simpler proof (some things hold in Banach spaces and, consequently, in Hilbert spaces as well, but in Hilbert spaces the proof may much simpler).

Also, there may be historic reasons. Finally, I have a vague feeling that a "theorem" is more than just the statement of the assertion. The same theorem may come in different versions, sometimes equivalent, sometimes slightly different, but they all present a general more abstract idea.