On 8/28/2022 6:38 PM, W. Neal Lewis wrote:
I will agree that by mathematical logic, Assets-(Liabilities)=Equity. ∴ Assets+(Liabilites)-(Liabilities)=Equity+Liability, or stated more simply, A=Eq+L. I have added Liability to both sides ∴ both sides remain equal.

However, although (A+L)=Eq, (A+L)≠Eq+(I+Ex). I have added a term to the right side that is most decidedly not on the left ∴ they cannot be equal.

Income and expenses are of fundamental type equity (they just haven't yet been combined with equity). They are also of opposite sense. Expenses are debit and Income is credit. When you add income to equity, you are increasing equity (equity is of sense credit). But when you add expenses to equity you are decreasing equity (because the sense of expenses is debit.

Assets = Equity + Liabilities   << the fundamental equality at the start >>

Now at the start, there are yet no items of income or expense, so those totals are zero. So no violation of anything if we add zero twice to the right hand side.

Assets = Equity + liabilities + Income - Expenses    << that's just Assets = Equity + Liabilities + (0) - (0)   and we are always allowed to add or subtract zero, no violation yet >>

We will now look at two transactions, one for an item of income of x and one for an item of expense of y. When we enter the item of income we would be debiting an asset account by x and crediting an income account by y. So ......

Assets + x = Equity + Liabilities + (0 + x) - (0)

And when we pay an expense of y we will be debiting an expense account by y and crediting an account of type asset by y  But remember, the normal sense of assets is debit and the normal sense of expenses is debit. Sp ....

Assets + x -y = Equity + Liabilities + (0 + x) - (0 + y)

OK now?

Michael D Novack

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