continuity
Mathematical tool for solving and verifying continuity problems in real analysis.
Install
mkdir -p .claude/skills/continuity && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/3008" && unzip -o skill.zip -d .claude/skills/continuity && rm skill.zipInstalls to .claude/skills/continuity
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for continuity in real analysisKey capabilities
- →Computes function limits at specific points
- →Verifies continuity conditions for piecewise functions
- →Performs one-sided limit calculations
- →Proves continuity theorems using logic solvers
How it works
It uses a symbolic math backend to calculate limits and a constraint solver to verify the identity of the limit and function value.
Inputs & outputs
When to use continuity
- →Check function limit at a point
- →Verify continuity of piecewise functions
- →Compute left and right limits
- →Prove continuity theorems
About this skill
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.
When not to use it
- →Numerical simulation or graphing of functions
- →Non-real-analysis mathematical problems
Prerequisites
Limitations
- →Limited to functions representable by SymPy
- →Requires explicit function definition to calculate limits
How it compares
It performs exact limit calculation rather than estimating via sampling or manual computation.
Compared to similar skills
continuity side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| continuity (this skill) | 1 | 7mo | Review | Intermediate |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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