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Explanation mechanisms from the field of Counterfactual Thinking are a widely-used paradigm for Explainable Artificial Intelligence (XAI), as they follow a natural way of reasoning that humans are familiar with. However, all common approaches from this field are based on communicating information about features or characteristics that are especially important for an AI's decision. We argue that in order to fully understand a decision, not only knowledge about relevant features is needed, but that the awareness of irrelevant information also highly contributes to the creation of a user's mental model of an AI system. Therefore, we introduce a new way of explaining AI systems. Our approach, which we call Alterfactual Explanations, is based on showing an alternative reality where irrelevant features of an AI's input are altered. By doing so, the user directly sees which characteristics of the input data can change arbitrarily without influencing the AI's decision. We evaluate our approach in an extensive user study, revealing that it is able to significantly contribute to the participants' understanding of an AI. We show that alterfactual explanations are suited to convey an understanding of different aspects of the AI's reasoning than established counterfactual explanation methods.