Thread: Determine whether these are valid arguments

1) If is a positive real number, then is a positive real number. Therefore, if is positive, where is a real number, then is a positive real number.
2) If , where is a real number, then . Let a be areal number with ; then

Originally Posted by ilovemymath

1) If is a positive real number, then is a positive real number. Therefore, if is positive, where is a real number, then is a positive real number.

This is not valid.

Originally Posted by ilovemymath

2) If , where is a real number, then . Let a be areal number with ; then

The words "if", "then", "where", etc. don't cease to have their usual meanings because they are used in a mathematical context. Consider this argument: "If x has gills, where x is a vertebrate, then x lives in water. Let Blinky be a vertebrate with gills; then Blinky lives in water."

This is not valid since a^2 is positive whether a is positive or negative...