Last Thursday
Patcher - Multiplying by ∞
3
9
0
Shared Last Thursday
About the preset, this one is processed via stereo plugins, oh and Fruity LSD is a very underrated plugin.
Part 2 of Synth - ∞;
Infinity isn't a regular number you can just multiply like 2 or 3. It's a concept that expresses "unbounded" size. Here are a few real, concrete ways people make sense of “multiply by infinity,” written plainly.
Extended real numbers
Idea: Treat infinity as a symbol (+∞ or −∞) appended to the real line.
Practical rule: Any positive finite number times +∞ gives +∞; any negative finite number times +∞ gives −∞. Zero times +∞ is indeterminate.
Examples: 3 × (+∞) = +∞, (−2) × (+∞) = −∞, 0 × (+∞) is undefined.
Limits (the rigorous way analysts use it)
Idea: Instead of multiplying by a symbol, look at what happens when one factor grows without bound.
Practical rule: If a_n → a (a finite number) and b_n → ∞, then a_n·b_n behaves like:
→ +∞ if a > 0,
→ −∞ if a < 0,
indeterminate if a = 0 (depends on how fast b_n grows relative to a_n).
Examples: lim_{n→∞} 3·n = ∞. lim_{n→∞} (1/n)·n = 1, which shows “∞×0” can give a finite number depending on rates.
Cardinal arithmetic (infinity as size of sets)
Idea: Infinity can mean “how many” elements a set has (cardinality). Multiplication is about forming ordered pairs.
Practical rule: For infinite cardinals κ and any finite n>0, κ × n = κ. For many infinite cardinals (like countably infinite ℵ0), κ + κ = κ and κ × κ = κ.
Example: ℵ0 × 2 = ℵ0 (doubling a countably infinite set is still countably infinite).
Extended algebraic systems (projective line, formal symbols)
Idea: Some systems add a single ∞ or two-sided infinities and give rules for algebraic convenience, but they’re not full arithmetic systems, some expressions stay undefined.
Practical note: These systems are tools, not contradictions to ordinary arithmetic.
Adequate and reasoning presets from now on.
=VYRA
Part 2 of Synth - ∞;
Infinity isn't a regular number you can just multiply like 2 or 3. It's a concept that expresses "unbounded" size. Here are a few real, concrete ways people make sense of “multiply by infinity,” written plainly.
Extended real numbers
Idea: Treat infinity as a symbol (+∞ or −∞) appended to the real line.
Practical rule: Any positive finite number times +∞ gives +∞; any negative finite number times +∞ gives −∞. Zero times +∞ is indeterminate.
Examples: 3 × (+∞) = +∞, (−2) × (+∞) = −∞, 0 × (+∞) is undefined.
Limits (the rigorous way analysts use it)
Idea: Instead of multiplying by a symbol, look at what happens when one factor grows without bound.
Practical rule: If a_n → a (a finite number) and b_n → ∞, then a_n·b_n behaves like:
→ +∞ if a > 0,
→ −∞ if a < 0,
indeterminate if a = 0 (depends on how fast b_n grows relative to a_n).
Examples: lim_{n→∞} 3·n = ∞. lim_{n→∞} (1/n)·n = 1, which shows “∞×0” can give a finite number depending on rates.
Cardinal arithmetic (infinity as size of sets)
Idea: Infinity can mean “how many” elements a set has (cardinality). Multiplication is about forming ordered pairs.
Practical rule: For infinite cardinals κ and any finite n>0, κ × n = κ. For many infinite cardinals (like countably infinite ℵ0), κ + κ = κ and κ × κ = κ.
Example: ℵ0 × 2 = ℵ0 (doubling a countably infinite set is still countably infinite).
Extended algebraic systems (projective line, formal symbols)
Idea: Some systems add a single ∞ or two-sided infinities and give rules for algebraic convenience, but they’re not full arithmetic systems, some expressions stay undefined.
Practical note: These systems are tools, not contradictions to ordinary arithmetic.
Adequate and reasoning presets from now on.
=VYRA
25 
140 
6 
