# 会计学理论 Accounting Theory ACFI202

Given two vectors $d$ and $c$ with $n$ components each, let $\min (d, c)$ be the vector whose $i$-th component is the minimum of the $i$-th components of $d$ and $c$ for $i=1, \ldots$, n. For example:
$$\min ((3,7,2),(0,5,3))=(0,5,2)$$
If $d$ and $c$ are nonnegative, then $d-\min (d, c)$ and $c-\min (d, c)$ are both nonnegative, and:
$$[d / / c]=[d-\min (d, c) / / c-\min (d, c)]$$
For instance:
\begin{aligned} {[(3,7,2) / /(0,5,3)] } &=[(3,7,2)-(0,5,2) / /(0,5,3)-(0,5,2)] \ &=[(3,2,0) / /(0,0,1)] . \end{aligned}

## ACFI202 COURSE NOTES ：

where one might note the difference between the $\mathrm{T}$-account $A s s e t s(T+1)$ and the vector $A S S E T S(T+1)$. The liabilities are:
\begin{aligned} \text { Liabilities }(T+1) &=[(0, \ldots, 0) / /(0, \ldots, 0, D)] \ &=[(0, \ldots, 0) / / \operatorname{DEBTS}(T+1)] \end{aligned}
Hence the end-of-the-period resultant equation zero-term is:
Assets
$$[(\ldots, 0, C A S H(T+1), F G(T+1), R M(T+1), 1,0,0) / /(0, \ldots)]$$
Liabilities
$$+[(0, \ldots, 0) / /(0, \ldots, 0, D)]$$
Total Assets and Liabilities
$$\begin{gathered} +[(0, \ldots, 0, D) / /(\ldots, 0, C A S H(T+1), F G(T+1) \ R M(T+1), 1,0,0)] \end{gathered}$$