In this paper we explore the influence of students' personalized notion of Fsmall_ numbers based on real life experiences on their understanding of limits. Tests were conducted on two samples of students. The first sample, consisting of students in the XII grade, had been taught limits using an informal approach (i.e., without recourse to the À definition) and the second sample, consisting of first year undergraduates, had been taught the formal À definition of limits. Our research points out that most students in both samples round off to zero such Fsmall numbers_ while evaluating limits wherever such numbers might occur because they perceive limit as a process of approximation.

<p>For decades, millions of people have been waiting for the "big one" in either Tokyo, Istanbul or Los Angeles. No one is able to predict where and when such a disaster will happen first. People expect it as a self-evident fact, will experience it as a stroke of fate, and will speak of it as a “tragedy”.</p> <p>Our aim cannot be (yet?) to predict where and when major earthquakes will occur, because that would amount to claiming to be able to announce in advance where and when the lightning strikes. Nevertheless, we believe that our understanding of the seismic process and associated risk should greatly benefit from the following question: what parameters control whether a dynamic rupture nucleates, grows or stops?</p> <p>It is crucial to understand the processes and conditions causing the initial stages of catastrophic rock tearing under pressure, and the interplay between mineral- and tectonic-scale factors. Both fluid percolation events and transformation-driven stress transfers can trigger mechanical instabilities ultimately causing rupture nucleation. And once a rupture has nucleated, similar processes should also occur within the damage zone and modulate the ability of small ruptures to “self-propagate” towards large seismic events.</p> <p>Our lack of understanding is considerable about the exact conditions for rupture nucleation and dynamic propagation. While observational methods help image mechanical instabilities, laboratory experiments provide insights on the physics of the lubrication processes enabling seismic faults to grow under pressure. Unfortunately, there remains a significant gap in scientific communication between researchers using different analytical methods or conceptual views.</p> <p>Here we outline transdisciplinary connections between the contributions to the session. From seismology to electrical conductivity measurements in the laboratory, from field geology to numerical modelling, from machine learning to mineralogy, from geodesy to mineral physics, here we walk on the frontier of knowledge in order to reshape the central questions that we need to ask to further investigate the rupture phenomenon.</p>