This is a fascinating challenge! Using only the digits 2, 0, 2, and 5 along with mathematical symbols, let's start by generating some numbers creatively. We’ll use operations like factorials, double factorials, square roots, and exponents strategically.

Examples:

1. 1: $5 - 2 - 2 + 0 = 1$
2. 2: $(5 - 2 - 0) / 2 = 2$
3. 3: $(5 - 2) \times (2/2) = 3$
4. 4: $(5 - 2) + (2 - 0) = 4$
5. 5: $5 + 0 + 2 - 2 = 5$
6. 6: $5 + (2 - 2) \times 2 = 6$
7. 7: $5 + 2 \times 1 = 7$ (with $1$ derived from $5 - 2 - 2 + 0$)
8. 8: $(5 - 2) + 2 + 2 - 0 = 8$
9. 9: $5 + 2 + 2 = 9$
10. 10: $5 + 5 \times (2-2) = 10$

Techniques:

• Factorials: $2! = 2$, $2!! = 2$
• Square roots and exponents: $\sqrt{4} = 2$
• Combination of expressions: Using expressions like $(x \times y) - z$ to adjust the result.

Approach:

To generate numbers up to 100, we need to utilize:

• Factorials for larger numbers and zero (since $0! = 1$)
• Double factorials for even/odd sequences.
• Exponentiation: Using $5^0 = 1$ and $5^2 = 25$.
• Creative arithmetic combinations.

We will build up incrementally using the constraints effectively. Let's continue with more numbers and see patterns that allow scaling towards 100.

Would you like to continue building more numbers step by step, or explore specific combinations for numbers like 20, 50, or 100? Let me know how you'd like to proceed!