# Suggestion for solution for some paradoxes in Mathematics.

#### Barendon223

##### New member
To put an end to some paradoxes in mathematics;
1. Infinity would not have to be regarded or used as a number, but rather as a limit only, unlike all real numbers that are both numbers and limits. Where infinity is already used in place of a number, a symbol to show it as a limit would have to be used just as it is used in discussing limits or calculus. This would put an end to discussions like whether 0.999... is equal to 1 or not.
2. The criteria of how sets form in some cases like in multivalued functions would have to be stated. For example, the square root of a positive real number x forms the set {y,-y} such that y^2 =x and (-y)^2 =x. The set {y,-y} exists only if absolute values of the elements are considered. Based on actual values, if the square root of x ={y,-y}, then since the square root of x=y and the square root of x=-y, this means y is a set containing square root of x and also -y is a set containing square root of x. This is not true.

#### Otis

##### Elite Member
Hi Barendon. Regarding #1, those paradoxes were resolved a long time ago. For example, many different proofs exist for [imath]0.\bar{9}=1[/imath]. And, people who treat infinity as a Real number don't understand the definition.

I need help understanding your point, in #2. For example: "The set {y,-y} exists only if absolute values of the elements are considered."

#### Barendon223

##### New member
Hi Barendon. Regarding #1, those paradoxes were resolved a long time ago. For example, many different proofs exist for [imath]0.\bar{9}=1[/imath]. And, people who treat infinity as a Real number don't understand the definition.

I need help understanding your point, in #2. For example: "The set {y,-y} exists only if absolute values of the elements are considered."

thank you for the suggestions