How to use directional infinity safely inside real symbolic workflows.
This final page gives ready-to-use, minimal, clean Python examples that demonstrate how SSM-Infinity works in actual symbolic workflows.
All examples below use only the public v1.0 engine (ssm_infinity_core.py).
1. Creating Directional Infinity
from ssm_infinity_core import SymbolicInfinity
# +∞ with posture 0.6
x = SymbolicInfinity(+1, 0.6)
# -∞ with posture -0.3
y = SymbolicInfinity(-1, -0.3)
print(x)
print(y)
Output:
<+∞, a=0.600000>
<-∞, a=-0.300000>
2. Addition & Subtraction
x = SymbolicInfinity(+1, 0.8)
y = SymbolicInfinity(-1, 0.2)
print(x + y) # zero-class or infinite-class
print(x - y) # infinite-class (direction depends on posture)
Behaviour:
- Same sign → infinite-class
- Opposite signs → zero-class
- Alignment is preserved via atanh/tanh merging.
3. Multiplication
x = SymbolicInfinity(+1, 0.4)
print(x * 5) # infinite-class (+∞)
print(x * -2) # infinite-class (-∞)
print(x * 0) # zero-class
Interpretation:
- Multiplying by positive → direction stays
- Multiplying by negative → direction flips
- Multiplying by zero → zero-class (deterministic)
4. Division
x = SymbolicInfinity(-1, 0.7)
y = SymbolicInfinity(-1, 0.2)
print(x / y) # finite-class
print(x / 3) # infinite-class
print(x / 0) # undefined
Division has clean symbolic outcomes:
- ∞ / ∞ → finite-class
- finite / ∞ → zero-class
- ∞ / 0 → undefined (only undefined case)
5. Exponentiation
x = SymbolicInfinity(+1, 0.9)
print(x ** 3) # infinite-class
print(x ** -4) # zero-class
Meaning:
- Positive exponent → infinite-class
- Negative exponent → zero-class
- Lane remains stable and bounded
6. Unary Operations
x = SymbolicInfinity(+1, 0.5)
print(-x) # <−∞, posture preserved>
Negation flips direction but keeps posture.
7. Using SSM-Infinity in Calculus / Asymptotics
Example: symbolic asymptotic comparison.
f = SymbolicInfinity(+1, 0.2) # slower divergence
g = SymbolicInfinity(+1, 0.9) # sharper divergence
print(f - g) # zero-class or finite-class, depending on posture
print(f + g) # infinite-class with merged alignment
Now asymptotic comparisons carry posture rather than becoming undefined.
8. Pattern for Safe Integration in Pipelines
To integrate SSM-Infinity into symbolic pipelines:
def safe_combine(a, b):
# Accept real numbers or infinite values
if isinstance(a, SymbolicInfinity) or isinstance(b, SymbolicInfinity):
return a + b
return a + b # classical fallback
This pattern lets SSM-Infinity sit beside any classical system.
9. The Universal Rule
Every expression will always evaluate to one of:
("infinite-class", SymbolicInfinity)
("zero-class", lane)
("finite-class", lane)
("undefined", None)
Nothing else is possible.
This is the clean, closed algebra that makes SSM-Infinity mathematically safe.
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Disclaimer
This page demonstrates symbolic usage patterns of Shunyaya Symbolic Mathematical Infinity (SSM-Infinity) and is not intended for operational or critical decision-making.
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