# Largest interval where solution is continuous

1. Mar 10, 2013

### 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?

2. Mar 10, 2013

### Zondrina

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

3. Mar 10, 2013

### 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.

4. Mar 10, 2013

### tiny-tim

Hi 1MileCrash!
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.

5. Mar 10, 2013

### 1MileCrash

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

6. Mar 10, 2013

### tiny-tim

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

7. Mar 10, 2013

### Dick

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

8. Mar 10, 2013

### 1MileCrash

Oh, now I guess we are getting somewhere.

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

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

9. Mar 10, 2013

### Dick

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

10. Mar 10, 2013

### 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.

11. Mar 10, 2013

### Dick

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.