| name | continuity |
|---|---|
| description | Problem-solving strategies for continuity in real analysis |
| allowed-tools | ["Bash", "Read"] |
Continuity
When to Use
Use this skill when working on continuity problems in real analysis.
Decision Tree
-
Check Definition - f(a) exists (function defined at point) - lim_{x->a} f(x) exists - lim_{x->a} f(x) = f(a)
-
Use SymPy for Limit Check -
sympy_compute.py limit "f(x)" --var x --at a- Compare with f(a) -
Piecewise Functions - Check left and right limits separately -
sympy_compute.py limit "f(x)" --var x --at a --dir left -
Verify with Z3 -
z3_solve.py prove "limit_exists implies continuous"
Tool Commands
Sympy_Limit
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a
Sympy_Limit_Left
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a --dir left
Z3_Prove
uv run python -m runtime.harness scripts/z3_solve.py prove "continuous_at_a"
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.