rubicanjr/continuity
skills/math/real-analysis/continuity/SKILL.md
Problem-solving strategies for continuity in real analysis
research
Updated Apr 22, 2026
$ install --global
skillsauthnpx skillsauth add rubicanjr/FinCognis continuityInstall this skill globally with one command. Works with Claude Code, Cursor, and Windsurf.
Security Scan Results
3 of 9 scanners reported clean
Some scanners were skipped, did not run, or reported a non-clean status. Review each row below.
3
Scanners Passed
9
Scanners in report
Clean
TrivyContainer and dependency vulnerability scanner
95%
Clean
SemgrepStatic code analysis for vulnerabilities
95%
Clean
mcp-scan (Snyk)Model Context Protocol security validation
95%
Skipped
Snyk (dep)Open source security scanning
50%
Skipped
Socket.devSupply chain security analysis
50%
Skipped
VirusTotalMulti-engine malware detection
50%
Skipped
CrowdStrikeAdvanced threat intelligence
50%
Skipped
OSV-ScannerOpen Source Vulnerability database check
50%
Skipped
OWASP Dep-Check
50%
Last scanned: Apr 22, 2026, 7:10 AM113.0s1 file scanned
SKILL.md
- 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.
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