Limit, continuity !

[Kieran]

Use the number 3559. Using all four each time form expressions for the consecutive numbers from one up.
Any arithmetical symbols may be used, but no summation or factorial symbols, no words also. Don't forget decimals, powers and roots! eg, 59- 5 + 3 is a solution for 57. What is the limit without a break in continuity ? The answer is 90, I am a bit lost !
Is there a formula that could be used ? How about a cayley table ? I assume a knowledge of group theory might help. The question was asked as part of an aptitude test . Cheers for any assistance offered.

 

[stapel]

Use the number 3559. Using all four each time....

"Using all four" what "each time"? You've only been given the one number. Or do you mean "using all four digits"?

...form expressions for the consecutive numbers from one up.

What are "the consecutive numbers"? You don't seem to have included a listing. Or do you mean "consecutive natural numbers, starting with the number 1"?

Any arithmetical symbols may be used, but no summation or factorial symbols, no words also. Don't forget decimals, powers and roots!

Does "symbols" include grouping symbols?

What is the limit without a break in continuity ?

"Limit" and "continuity" mean very specific things in mathematics. But I don't think you are intending those meanings here. Do you perhaps mean to ask for the greatest value whose expression you can form, before you finally hit the first value whose expression you can not form?