And “What they will end up doing” is yet another disconnected set.

View from the Solent

SE, It’s likely that â€śWhat they will end up doing” will have some overlap with the “politically feasible”. But the intersection of the 3 will still be the null set.

Surreptitious Evil

I strongly suspect only with a time shift. What they will end up doing will be politically feasible at the time but would not be if proposed now.

Chris

And yet Krugman thinks that the USA needs an even bigger stimulus because the first one didn’t work. Same Venn diagram, I think.

Unimportant Quibbler

View from the Solent: I make this mistake all the time, and sometimes people pick me up on it. Back in the old days “null set” meant {} – the set with nothing at all in it. But these days the term “null set” has been appropriated by the measure-theory people (it now means a set that is “almost empty” in some sense, although may contain an infinite number of sparsely-distributed items) and {} is referred to exclusively as the “empty set”. I still slip into the old terminology by force of habit but I understand that financial mathematicians, probabilists etc would just titter at me for doing so.

David Gillies

UQ, by ‘almost empty’ you presumably mean a set that is nowhere dense*, i.e. of Lebesgue measure zero? I’ve always used the term ’empty set’ for the set containing no objects and Ø or {} to refer to it (helpfully, Mathematica uses the latter convention.)

* e.g. the set of real numbers whose continued fraction coefficients do not yield Khinchin’s constant.

Unimportant Quibbler

DG – exactly correct, but I wished to remain non-technical as I doubted VftS would follow all this talk about Lebesgue measures đź™‚

My teachers usually called the empty set the “null set”, and according to wikipedia (and the occasional older textbook I have hanging about) that used to be acceptable standard terminology. But no longer, since that’s been appropriated by the measure-theory people and no longer needs to be empty!

So Much For Subtlety

View from the Solent – “Itâ€™s likely that â€śWhat they will end up doingâ€ť will have some overlap with the â€śpolitically feasibleâ€ť. But the intersection of the 3 will still be the null set.”

I am not so sure. I think that you need to add a picture of a bicycle pump labeled “Economic Pain” with three tubes leading to each balloon. At the moment there may be no overlap, or if there is, the overlap is empty. But as the pain increases, the three will eventually have an overlap containing at least one option.

So true!

And “What they will end up doing” is yet another disconnected set.

SE, It’s likely that â€śWhat they will end up doing” will have some overlap with the “politically feasible”. But the intersection of the 3 will still be the null set.

I strongly suspect only with a time shift. What they will end up doing will be politically feasible at the time but would not be if proposed now.

And yet Krugman thinks that the USA needs an even bigger stimulus because the first one didn’t work. Same Venn diagram, I think.

View from the Solent: I make this mistake all the time, and sometimes people pick me up on it. Back in the old days “null set” meant {} – the set with nothing at all in it. But these days the term “null set” has been appropriated by the measure-theory people (it now means a set that is “almost empty” in some sense, although may contain an infinite number of sparsely-distributed items) and {} is referred to exclusively as the “empty set”. I still slip into the old terminology by force of habit but I understand that financial mathematicians, probabilists etc would just titter at me for doing so.

UQ, by ‘almost empty’ you presumably mean a set that is nowhere dense*, i.e. of Lebesgue measure zero? I’ve always used the term ’empty set’ for the set containing no objects and Ø or {} to refer to it (helpfully, Mathematica uses the latter convention.)

* e.g. the set of real numbers whose continued fraction coefficients do not yield Khinchin’s constant.

DG – exactly correct, but I wished to remain non-technical as I doubted VftS would follow all this talk about Lebesgue measures đź™‚

My teachers usually called the empty set the “null set”, and according to wikipedia (and the occasional older textbook I have hanging about) that used to be acceptable standard terminology. But no longer, since that’s been appropriated by the measure-theory people and no longer needs to be empty!

View from the Solent – “Itâ€™s likely that â€śWhat they will end up doingâ€ť will have some overlap with the â€śpolitically feasibleâ€ť. But the intersection of the 3 will still be the null set.”

I am not so sure. I think that you need to add a picture of a bicycle pump labeled “Economic Pain” with three tubes leading to each balloon. At the moment there may be no overlap, or if there is, the overlap is empty. But as the pain increases, the three will eventually have an overlap containing at least one option.