Best use case
continuity is best used when you need a repeatable AI agent workflow instead of a one-off prompt.
Problem-solving strategies for continuity in real analysis
Teams using continuity should expect a more consistent output, faster repeated execution, less prompt rewriting.
When to use this skill
- You want a reusable workflow that can be run more than once with consistent structure.
When not to use this skill
- You only need a quick one-off answer and do not need a reusable workflow.
- You cannot install or maintain the underlying files, dependencies, or repository context.
Installation
Claude Code / Cursor / Codex
Manual Installation
- Download SKILL.md from GitHub
- Place it in
.claude/skills/continuity/SKILL.mdinside your project - Restart your AI agent — it will auto-discover the skill
How continuity Compares
| Feature / Agent | continuity | Standard Approach |
|---|---|---|
| Platform Support | Not specified | Limited / Varies |
| Context Awareness | High | Baseline |
| Installation Complexity | Unknown | N/A |
Frequently Asked Questions
What does this skill do?
Problem-solving strategies for continuity in real analysis
Where can I find the source code?
You can find the source code on GitHub using the link provided at the top of the page.
SKILL.md Source
# Continuity
## When to Use
Use this skill when working on continuity problems in real analysis.
## Decision Tree
1. **Check Definition**
- f(a) exists (function defined at point)
- lim_{x->a} f(x) exists
- lim_{x->a} f(x) = f(a)
2. **Use SymPy for Limit Check**
- `sympy_compute.py limit "f(x)" --var x --at a`
- Compare with f(a)
3. **Piecewise Functions**
- Check left and right limits separately
- `sympy_compute.py limit "f(x)" --var x --at a --dir left`
4. **Verify with Z3**
- `z3_solve.py prove "limit_exists implies continuous"`
## Tool Commands
### Sympy_Limit
```bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a
```
### Sympy_Limit_Left
```bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a --dir left
```
### Z3_Prove
```bash
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.Related Skills
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