Vibecosystem continuity

Problem-solving strategies for continuity in real analysis

install

source · Clone the upstream repo

git clone https://github.com/vibeeval/vibecosystem

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/vibeeval/vibecosystem "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/math/real-analysis/continuity" ~/.claude/skills/vibeeval-vibecosystem-continuity && rm -rf "$T"

manifest: skills/math/real-analysis/continuity/SKILL.md

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.