Problem of identity and quadratic equation

Abhishek Majhi (1) , Ramkumar Radhakrishnan (2)

1 Indian Statistical Institute [Kolkata]
2 Sardar Vallabhbhai National Institute of Technology [Surat]

Given "ab = 0", considering the arithmetic truth "0.0 = 0" we conclude that one possibility is "both a = 0 and b = 0". Consequently, the roots of a quadratic equation are mutually inclusive. Therefore, the concerned variable can acquire multiple identities in the same process of reasoning or, at the same time. The law of identity gets violated, which we call the problem of identity. In current practice such a step of reasoning is ignored by choice, resulting in the subsequent denial of "0.0 = 0". Here, we deal with the problem of identity without making such a choice of ignorance. We demonstrate that the concept "identity of a variable" is meaningful only in a given context and does not have any significance in isolation other than the symbol, that symbolizes the variable, itself. We demonstrate visually how we actually realize multiple identities of a variable at the same time, in practice, in the context of a given quadratic equation. In this work we lay the foundations, based on which we intend to bring forth some hitherto unattended facets of reasoning that concern two basic differential equations which are pivotal to the literature of physics.

Mots clés: Visual mathematics; Quadratic equation; Identity; Contextual truth

Domaines: Mathématiques [math]

Abhishek Majhi, Ramkumar Radhakrishnan. Problem of identity and quadratic equation. 2022. ⟨hal-03554501⟩