Boolean algebraic structure on [0,1]

Abstract

Firstly, we show that the famous problem of “Can the unit interval [0,1] be equipped with a Boolean algebraic structure?” is an ill-posed problem. In this sense, we notice that the conventional answer for this problem “[0,1] cannot be equipped with a Boolean algebraic structure” has no value in itself. We argue that we need additional conditions to answer the above problem legitimately.

Secondly, we propose a new non-standard model of real numbers.

Thirdly, we prove that, based on this new model, there is an algorithm to define a Boolean algebraic structure on [0,1].

Keywords:

• Operators
• algebra
• logic
• analysis
• AI

C.R.Categories:

• I.2.3
• F 4.1