purposeLessConditionDev.md

Deduction 🧠

I've uploaded this document before the ending date of the audit thus, so as to no-one copies my finding, this document has limited information. To contextualize this math prodecure you should read all the text in my finding first. ❗❗❗

📘 Note ℹ️ TEXT IN FINDING.

LaTeX Display:

$\frac{s}{C} \cdot e_c \cdot t - d \cdot \frac{s}{C} \cdot e_c \cdot t \geq \frac{s}{O} \cdot e_O \cdot t + \frac{d \cdot e_c \cdot t}{n_O}$

Classic Keyboard Display: (s / C) * e_C * t - d * (s / C) * e_C * t >= ((s / O) * e_O * t) + (d * e_C * t) / n_O

Simplification Steps 👣

0️⃣. Add the fractions on the right side

LaTeX Display:

$\frac{s}{C} \cdot e_c \cdot t - d \cdot \frac{s}{C} \cdot e_c \cdot t \geq \frac{ n_o \cdot s \cdot e_o \cdot t + O \cdot d \cdot e_c \cdot t}{O \cdot n_O}$

Classic Keyboard Display: (s / C) * e_C * t - d * (s / C) * e_C * t >= (n_O * s * e_O * t + O * d * e_C * t) / O*n_O

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1️⃣. Factorize ( s ) , ( e_C ) , ( t ) and ( 1/C ) on the left and ( t ) on the right.

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LaTeX Display:

$\frac{s}{C} \cdot e_c \cdot t \cdot (1 - d) \geq t \frac{(n_o \cdot s \cdot e_o + O \cdot d \cdot e_c)}{O \cdot n_O}$

Classic Keyboard Display: (s / C) * e_C * t * (1 - d) >= t * ((n_O * s * e_O + O * d * e_C) / O*n_O)

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2️⃣. ( t ) can be cancelled out.

LaTeX Display:

$\frac{s}{C} \cdot e_C \cdot (1 - d) \geq \frac{(n_O \cdot s \cdot e_O + O \cdot d \cdot e_c)}{O \cdot n_O}$

Classic Keyboard Display: (s/C) * e_C * (1 - d) >= (n_O * s * e_O + O * d * e_C ) / O*n_O

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3️⃣. Multiply both sides by ( C ) and ( O * n_O )

LaTeX Display:

$O \cdot n_O \cdot s \cdot e_C \cdot (1 - d) \geq ( n_O \cdot s \cdot e_O + O \cdot d \cdot e_C ) \cdot C$

Classic Keyboard Display: O * n_O * s * e_C * (1-d) >= (n_O * s * e_O + O * d * e_C) * C

🚧 Note: ⚠️ TEXT IN THE FNDING.

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4️⃣. Compute the right side multiplication and then leave all the factors that (s) is multiplying on the right side of the equation and factors without (s) in the left side. Notice we can factor out (n_O) and (s)

LaTeX Display:

$- O \cdot d \cdot e_C \cdot C \geq (C \cdot e_O - O \cdot e_C \cdot (1 - d)) \cdot s \cdot n_O$

Classic Keyboard Display: -O * d * e_C * C >= (C * e_O - O * e_C (1-d)) * s * n_O

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5️⃣. TEXT IN THE FINDING

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6️⃣. TEXT IN THE FINDING

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LaTeX Display:

$\frac{-O \cdot d \cdot e_C \cdot C}{(C \cdot e_O - O \cdot e_C \cdot (1 - d))} \geq s \cdot n_O$

Classic Keyboard Display: (-O * d * e_C * C) / (C * e_O - O * e_C * (1-d)) >= s * n_o

7️⃣. TEXT IN THE FINDING

LaTeX Display:

$\frac{-O \cdot d \cdot e_C}{(C \cdot e_O - O \cdot e_C \cdot (1 - d))} \leq s \cdot n_O$

Classic Keyboard Display: (-O * d * e_C * C) / (C * e_O - O * e_C * (1-d)) <= s * n_o

TEXT IN THE FINDING:

$(C \cdot e_O - O \cdot e_C \cdot (1 - d)) > 0$

Classic Keyboard Display: C * e_o - O * e_c * (1-d) > 0