Pickles and use-by-date fears...

Hey there, I have a surplus of Korean Takuan-type pickles (I bought a big pack of beautiful sun-like slices) and was wondering how long one should keep them in the fridge? They're in a tupperware type thingy, but as there was no date on the packaging, I keep getting the fear - I have a bit of an obsession with use-by-dates, which my other half finds very odd. As they are preserved, I figured they could live in there for a while, but as I say...I got the fear now, and so keep using them in EVERY meal in my haste to get through 'em! I also have some plump umeboshi and some umeboshi puree, neither of which have a date on (possibly because I put the puree box in the recycling. D'oh.) so yet again - how long are they good for in the fridge? It's only me who'll have them; the man isn't keen on them, sadly. :(
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