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For those who were on the last thread concerning this, I have started a new one over since the last one is dead. I have thought on the rules for a while, and now have made a few new rules and changed the otherones.

For those who have not read the last thread, what I am trying to do is create a system so that [tex] \frac {a} {x} \cdot \frac {x} {1} = \frac {a} {1} [/tex] even if [tex] x = 0 [/tex]

It is finished.

Rules

First the order of operations must be revised.

The order will go

1)All workable exponents

2)All workable parentesis

3)Multiply and Divide with zeros

4)Solve for any [tex] \infty ^ 1 [/tex]

5)Normal multiplication and division

6)Normal addition and subtraction

7)Solve for any [tex] \infty ^ 0 [/tex]

Second the comunive property cannot be used until step 4 is applied.

Third [tex] a \infty ^ 1 = a [/tex] and [tex] a \infty ^ 0 = 0 [/tex] and to avoid complication [tex] 0 \neq 0 \infty ^ 0 [/tex]. This does allow [tex] a \cdot 0 = 0 [/tex]

Fourth comes the basic rules I started with [tex] \frac {a \infty ^ {x}} {0} = a \infty ^ {x + 1} [/tex]

and [tex] a \infty ^ x \cdot 0 = a \infty ^ {x-1} [/tex]

These are the basic rules.

Now for the other rules.

First, how to squareroot a [tex] \infty [/tex] number.

[tex] \sqrt {4} = 2 [/tex] need someone to show me how to do +/- sign.

so [tex] \sqrt {4 \infty ^ 1} = 2 \infty ^ 1 [/tex]

which is done by saying that [tex] \sqrt {a \infty ^ x} = \sqrt {a} \infty ^ {\sqrt{x}} [/tex]

Second of infinity numbers with different infinity powers. The rule goes [tex] a \infty ^ x \cdot b \infty ^y = a b \infty ^ {xy} [/tex]. This does work if [tex] x = y [/tex]

Third is addition and subtraction of numbers with different powers. The rule goes [tex] a \infty ^ x + b \infty ^ y = a \infty ^ x + b \infty ^ y [/tex].

Now if [tex] x = y [/tex] then [tex] a \infty ^ x + b \infty ^y = \left( a + b \right) \infty ^ x [/tex]

For those who have not read the last thread, what I am trying to do is create a system so that [tex] \frac {a} {x} \cdot \frac {x} {1} = \frac {a} {1} [/tex] even if [tex] x = 0 [/tex]

It is finished.

Rules

First the order of operations must be revised.

The order will go

1)All workable exponents

2)All workable parentesis

3)Multiply and Divide with zeros

4)Solve for any [tex] \infty ^ 1 [/tex]

5)Normal multiplication and division

6)Normal addition and subtraction

7)Solve for any [tex] \infty ^ 0 [/tex]

Second the comunive property cannot be used until step 4 is applied.

Third [tex] a \infty ^ 1 = a [/tex] and [tex] a \infty ^ 0 = 0 [/tex] and to avoid complication [tex] 0 \neq 0 \infty ^ 0 [/tex]. This does allow [tex] a \cdot 0 = 0 [/tex]

Fourth comes the basic rules I started with [tex] \frac {a \infty ^ {x}} {0} = a \infty ^ {x + 1} [/tex]

and [tex] a \infty ^ x \cdot 0 = a \infty ^ {x-1} [/tex]

These are the basic rules.

Now for the other rules.

First, how to squareroot a [tex] \infty [/tex] number.

[tex] \sqrt {4} = 2 [/tex] need someone to show me how to do +/- sign.

so [tex] \sqrt {4 \infty ^ 1} = 2 \infty ^ 1 [/tex]

which is done by saying that [tex] \sqrt {a \infty ^ x} = \sqrt {a} \infty ^ {\sqrt{x}} [/tex]

Second of infinity numbers with different infinity powers. The rule goes [tex] a \infty ^ x \cdot b \infty ^y = a b \infty ^ {xy} [/tex]. This does work if [tex] x = y [/tex]

Third is addition and subtraction of numbers with different powers. The rule goes [tex] a \infty ^ x + b \infty ^ y = a \infty ^ x + b \infty ^ y [/tex].

Now if [tex] x = y [/tex] then [tex] a \infty ^ x + b \infty ^y = \left( a + b \right) \infty ^ x [/tex]

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