Largest interval where solution is continuous

[1MileCrash]

"Largest interval where solution is continuous"

I have a gripe with the way I am being asked to do this.

I am given a DE and asked to select the "largest interval of t where the solution is continuous."

A: (0,1)
B: (5, infinity)
C: (-2, 0)
D: (-8,14)
Etc

But all intervals of t are obviously the same size. So wtf are they asking? The largest interval assuming I am 12 and don't understand the cardinality of the real numbers?

 

[STEMucator]

I have a gripe with the way I am being asked to do this.

I am given a DE and asked to select the "largest interval of t where the solution is continuous."

A: (0,1)
B: (5, infinity)
C: (-2, 0)
D: (-8,14)
Etc

But all intervals of t are obviously the same size. So wtf are they asking? The largest interval assuming I am 12 and don't understand the cardinality of the real numbers?

First off... what IS the DE? Then I can help perhaps.

 

[1MileCrash]

I don't recall, this was online homework and I am on my phone. It doesn't really matter. Assume more than one of those choices contains the initial condition and is an interval where the solution is continuous. Then the question has no answer.

I'm looking for an actual way to ask what they want. If I have to say things correct in proofs, I expect questions asked correctly too.

 

[tiny-tim]

Hi 1MileCrash!

I am given a DE and asked to select the "largest interval of t where the solution is continuous."

I 'll guess (without having seen the full question) that the given DE is continuous on only some of those choices.

Once you've found which choices are available, it may be obvious which is the largest one.

 

[1MileCrash]

How is some interval of reals larger than any other? Any interval of reals containss uncountably infinite members.

 

[tiny-tim]

[0,3] is obviously larger than [1,2]

 

[Dick]

How is some interval of reals larger than any other? Any interval of reals containss uncountably infinite members.

'largest' here doesn't mean cardinality. It means length.

 

[1MileCrash]

'largest' here doesn't mean cardinality. It means length.

Oh, now I guess we are getting somewhere.

So what about:

(-infinity, -3)
(42000, infinity)

These are the same cardinality and length too, and I had to make the choice in this situation as well.

 

[Dick]

Oh, now I guess we are getting somewhere.

So what about:

(-infinity, -3)
(42000, infinity)

These are the same cardinality and length too, and I had to make the choice in this situation as well.

No way to choose in that case. Unless the DE isn't continuous on one of them.

 

[1MileCrash]

I checked and it doesn't look like that situation occurs.

However, the book still instructs me to find the longest interval (with no choices.) While it is clearer because of the use of "longest," this question is still impossible to answer except for some obscure case, I'm sure.

 

[Dick]

I checked and it doesn't look like that situation occurs.

However, the book still instructs me to find the longest interval (with no choices.) While it is clearer because of the use of "longest," this question is still impossible to answer except for some obscure case, I'm sure.

If the book is really asking you to choose the longest interval between two infinite choices, then obviously, there is no way to choose. Unless one is contained in the other. In which case there is some justification for picking the one that contains the other.