continuity
Problem-solving strategies for continuity in real analysis
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- parcadei/Continuous-Claude-v3
- Last source activity
- January 10, 2026 at 01:54
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- English
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- Problem-solving strategies for continuity in real analysis
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# 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.
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